Drawing on an older answer I wrote on the commonness of the name:

There are in fact records of multiple persons with that name, and in fact there are several of them in the Bible. For starters, "Jesus" is not the name that the man would have been known by in his lifetime. "Jesus" is an Anglicization of Iēsūs, a Latinization of the Greek "Ἰησοῦς" (Iesous), which is itself the Greek form of the name Hebrew/Aramaic "Yēshūăʿ". Jesus, the son of Joseph, would have been known to those around him as "Yeshua ben Yoseph". To add another layer to this, Yeshu'a (יֵשׁוּעַ) is a form of the name "Y'hōshūă" (יְהוֹשֻׁעַ). Yehoshua in turn gets Anglicized as "Joshua", which leads eventually to the culmination here, namely that "Jesus" and "Joshua" are, through a convoluted path, the same name. The name itself derives from "God [Jah] is salvation".

There are in fact several persons then who bear this name in the Bible. The second-most famous of course would be Joshua, of "The Book of Joshua", and one of the great heroes of Jewish history, leading them into the promised land and defeating the Canaanites. In this light, giving your child the name of "Yeshua" or "Yehoshua" is not unlike the old practice in early America where the Founding Fathers provided inspiration for names of children like Washington Irving, or perhaps something like the common Armenian name of Haik, which harks back to their mythical founding figure.

Many other Joshuas (Yeshua/Yehoshua) existed in those times, such as the Biblical figure of the High Priest in the Book of Zechariah, as well as more tangible evidence such as tomb stones found on various graves in the region from the period. Ilan and Hünefeld provide a number more examples from various literature of the period such as Rabbinical writings and Josephus. Some of you will no doubt remember the minor news item from a decade ago around the 'Talpiot tomb' in Jerusalem which was revealed to have the names of Jesus, Mary, and Joseph present on ossuaries (it had been discovered years prior, but that year Discovery Channel did a nice sensationalist pseudo-history piece on it). Needless to say, controversy surrounds it, but at the very least a strong argument against it is the simple fact that none of the names present were particularly unique for the time. There are even multiple examples of "Yeshua‘ bar Yehosep” and similar derivations in epigraphy that most certainly doesn't refer to the Jesus. A similar ossuary also exists bearing "Ya'akov bar Yosef achui de Yeshua" ("James, son of Joseph, brother of Jesus") on it, and although there is strong suspicion surrounding it as being a more modern fraud, in any case, even if 'legitimate' it similarly can be explained by the commonality of such names.

In sum, the name was likely a fairly common one in Jewish communities of antiquity, but through the quirks of transliteration, the specific form of 'Jesus' has passed down as being fairly unique and stands out from the Joshuas, even though they wouldn't have at the time, and doesn't in the actual epigraphic evidence of the period.

Sources

Ayalon, Avner, Miryam Bar-Matthews, and Yuval Goren. "Authenticity examination of the inscription on the ossuary attributed to James, brother of Jesus." Journal of Archaeological Science 31, no. 8 (2004): 1185-1189.

Ilan, Ṭal & Kerstin Hünefeld. Lexicon of Jewish Names in Late Antiquity: The Eastern Diaspora 330 BCE-650 CE. Mohr Siebeck, 2002.

Meyers, Eric M. 2006. "The Jesus tomb controversy: An overview". Near Eastern Archaeology 69, (3) (Sep): 116-118,

Oxford English Dictionary. "Jesus" OED Online.

Rollston, Christopher A. "The Talpiyot (Jerusalem) Tombs: Some Sober Methodological Reflections on the Epigraphic Materials" The Jesus Discovery: The New Archaeological Find that Reveals the Birth of Christianity. Simon & Schuster, 2012.

As u/Georgy_K_Zhukov said, Ἰησοῦς was the Hellenisation of 'Joshua', which was a pretty common name, well known from inscriptions and historic individuals. An example would be the high priest of a.d. 65-66, Joshua ben Gamla. Josephus writes his name Ἰησοῦς, the same as the Gospel writers, while he is referred to in the Talmud as Yehoshua.

The other two names you mention though weren't common, and also weren't the Biblical individuals' birth names. 'Peter' is a Greek nickname meaning 'The Rock' (you are Peter, and on this rock I will build my church). In life he was probably known mostly as 'Kephas' the Aramaic translation of that name (it's what Paul generally calls him). He was born a Simon however, and Simons were common as anything. He wasn't even the only Simon among the 12 apostles, let alone the New Testament (Simon the magician for instance). The popularity of Simon probably owes a lot to the fact that it was a genuine Greek name which was very similar to (and was used interchangably with) the Patriarchal name Simeon. The vastly impressive 'Lexicon of Jewish Names in Late Antiquity' by Tal Ilan collects a considerable number of references to 'Simons', and finds that it was actually the most popular man's name for Jews in Palestine in the centuries around the Common Era (the Google Books preview is a bit limited, so I'll cite this guy who messes around with her data a bit, but basically follows it. You can see the Simon page though

'Paulus' is a Latin cognomen and nomen which Paul likely adopted because it was similar to his Jewish name of Sha'ul (after king Saul). The name wasn't unknown among diaspora Jews: Ilan finds another few examples of Jews or probable Jews using it (for instance a Paulus who bought a house in the Jewish quarter of Oxyrhynchus, Egypt).

Here's the link if you want to try and find it yourself, but search doesn't work (it thinks the entire book's in Greek).

Richard Bauckham, Jesus and the Eyewitnesses (2nd. ed. 2017) utilizes Tal Ilan, Lexicon of Jewish Names in Late Antiquity: Part I: Palestine 300 BC-200 CE (2002) to discuss the relative popularity of names amongst Palestinian Jews around the time of Jesus. Illan's Lexicon compiles the names of approximately 3,000 Palestinan Jews whose names are known through the works of Josephus, texts from Masada and the Judean desert, ossuary inscriptions, early rabbinic sources, and the New Testament itself. When compiling statistics, both Bauckham and Ilan exclude people who may not be Jewish and those who are Samaritans, those not born in Palestine, those who are fictitious, those who retained a Gentile name upon conversion, and those with names that were nicknames or family names. Bauckham largely follows Illan, but does not exclude some second names that Illan does and differs from her on certain assessments (such as whether certain persons are likely fictitious).

Bauckham reckons that we have access to "2626 occurrences of 447 male names and 328 occurences of 74 female names." Most people, especially women, had a relatively popular name. Over 15% of men and 28% of women had one of the two most popular names. Over 40% of men and almost 50% of women had one of the nine most popular names. Only approximately 8% of men and 10% of women had a name that only appears once in our sources.

From 330 BCE to 200 CE, Simon/Simeon was the single most popular name for male Palestinian Jews, with 243 recorded uses. Joseph/Joses is second, Lazarus is third, Judas is fourth, John is fifth, and Jesus is sixth. All are found in the Gospels or Acts. Jonathan, the eight most popular name, is the most popular that may not appear in the Gospels or Acts (appearing only in a variant reading of Acts 4:6). Ishmael, the 13th most popular name with thirty recorded uses, is the most popular to not appear in any version of the Gospels or Acts.

From 330 BCE to 200 CE, Mary and Salome were the by far most popular names for female Palestinian Jews, with 70 and 58 recorded uses respectively. Both appear in the Gospels or Acts. The third most common female name is Shelamzion, which does not appear in the Gospels or Acts and has only twenty four recorded uses.

Overall, the names present in the Gospels and Acts conform well to the distribution of names found elsewhere. The most common names in the Gospels and Acts generally line up with the most common names used elsewhere (with the biggest discrepancy being that the Gospels and Acts contain only one Lazarus despite its popularity) while relatively unique names are also present in smaller amounts.

Many of the most popular names appear to have been popular because they were shared by the Hasmonean royal family. Simon likely received a boost due to the close similarity between the Greek Simon and the Hebrew Simeon (many Jews of the period adopted a Greek/Latin name that sounded similar to their Hebrew name and naming a child Simeon would make this process incredibly simple). Some names were likely popular because they were theophoric and some names were likely popular due to a personal or nationalistic meaning.

It should be noted that naming conventions in the Diaspora differed greatly from naming conventions in Palestine. For example, the second most popular male name amongst Jewish inscriptions in Greco-Roman Egypt is Sabbataius, which is the 68th most popular name amongst Palestinain Jews (appearing only 5 times).