Many Biblical names were changed to more Anglicized versions, and a lot of them are commonly used in the Anglosphere today. Abraham's real name was Avraham, and his sons were Yitzhak and Yaakov, not Isaac and Jacob. Moses was in fact named Moshe. Other examples include Jonathan (Yonatan), Benjamin (Binyamin), Jesse (Yishai), Joseph (Yosef), etc.
Can anyone explain why the changes were done, and who did them?
There are a couple interrelating reasons here. No one specifically went out to change the names, they just changed. So there's no "who" or "why". To organize the reasons into a list:
So to start with #1, English has changed. All words in English have been subject to numerous sound changes over time. Perhaps the most important for that name list is the Great Vowel Shift. This changed several vowel English vowel sounds, and is a large part of what makes English spelling confusing. Before this vowel shift, the initial "a" in "Abraham" would've been pronounced as in Hebrew, but the Great Vowel Shift changed the English long-A from that sound to the modern English long-A we know and love.
Second, Hebrew has changed since some names were loaned. One example is the name "Samson", which in Hebrew is "Shimshon". The reason for the vowel difference is that Hebrew shifted "a" to "i" in certain contexts. This is also why the Arabic name Maryam and the English name Mary have an A where the name Miriam doesn't--Miriam was once Mariam, but Hebrew changed since those names were loaned into Greek. One example from your list is from "Jonathan". At one point, the letter tav in certain environments was pronounced "th", just the way B is sometimes V, p/f, k/kh (daled and gimmel also had two sounds at one point). In the time period where the biblical narratives take place, all these letters would've not yet split, but by the time the names were loaned (and when the system for writing vowels was fixed) the letters bgdkpt all had two sounds which varied according to phonetic context. Modern Hebrew does this with 3 of them, but some liturgical Hebrew pronunciations have more or less (the Ashkenazi tav/sav being one, the th became s)
Historical transliteration is actually a very important way of knowing ancient Hebrew pronunciations. It can be guessed at, for instance, that 'ayin was pronounced two different ways, just like shin and sin are. This is because in Greek the 'ayin in Ya'akov becomes null, while the 'ayin in Gemorrah becomes a gamma in Greek (which is why it's not 'amorah).
Third, names were adapted for different languages. Greek and Latin have no "sh", so they were approximated with "s". English names are sometimes derived or influenced by the Greek or Latin versions of those names. That's why Moshe has an s at the end in English, and why Solomon has that final n. Both of those are endings to make them work with how nouns are declined in Greek.
hi.. you might get something out of these related posts
Luke is short for Lucas. Why does the bible Luke only have the short form? - /u/vhcngh traces John, Jonathan, Luke, Mark and Matthew from English to Latin to Greek
Which came first, the name 'John' or 'Johnathan' (or similar spellings?) Were the Johns of biblical times simply called John or were they less famously named Johnathan? If John came first, how did it evolve to become the short version of Johnathan? - various respondents provide the original Hebrew names for John, Jonathan, Adam, Matthew and Paul
Was Jesus a common name when the biblical Jesus was alive? - lots of comments and links to other posts discussing the Hebrew name for Jesus
Biblical names like John,Paul,Gabriel or Peter have different pronunciations in other languages like Juan (John ,Spanish) or Paolo ( Paul, Italian). How were these names pronounced during biblical times? - very scanty information here, but a few more names are given
Because. I think there is no greater mystery than to make things easier for local people. Actually, all countries do it. In Spanish-speaking countries, some time ago, it was normal "hispanicize" the name of monarchs, nobles, church members or other important characters (Alberto Durero, Miguel Bakunin or Bernardo Montgomery, for example). But all countries do that: Pope Francis (English), Papa Francisco (Spanish), Papst Franziskus (German) Papiez Franciszek (Polish), etc.