Short version: Joshua is the Hebrew version of the Greek name Jesus (Jesús in Spanish), so the name is still commonly used in English.
Long version: The name יְהוֹשֻׁעַ (Yehoshu'a) is an old Hebrew name meaning 'Yahweh is salvation' and is commonly translated into English as Joshua. It is a rather common name in the Old Testament, the most famous being Joshua the Ephraimite, the successor to Moses as the leader of the Hebrew people.
The name Yehoshu'a has a diminutive form, יֵשׁוּעַ (Yeshu'a) -- sort of like someone named Robert being called Bob. So a person named Yehoshu'a may be called Yeshu'a by their friends and family.
Yeshu'a was then translated into Greek as Ἰησοῦς , which through Latin came into many European (especially Romance) languages as Jesus. But during his actual life, Jesus would have been called יְהוֹשֻׁעַ (Yehoshu'a) or יֵשׁוּעַ (Yeshu'a) -- or perhaps some Aramaic equivalent, as it's thought that would be the language he would have spoken, but I don't know that translation- not Jesus. Jesus is a name that came later through translation.
In Romance languages, both the common name and the historical/religious figure is known as Jesus, coming from the Greek translation. In Germanic languages, however, the historical/religious figure is still called Jesus (Jezus in Dutch, I believe), as Latin was the language of the church, but the common name is Joshua/Josh, using the original translation from Aramaic.
So in English, the original name of Jesus the person (יְהוֹשֻׁעַ) is still commonly used, in the form of the name Joshua. The name Jesus/Jesús is just a different translation of that original name via Greek.
It was because of the Muslim invasion of Spain during the middle ages. For 700 years the muslims controlled most of the Iberian peninsula. During that time the spaniards noticed that there were many muslim men named Muhammad, and so spanish families began to named their sons Jesus in order to distinguish themselves from the muslims. It became acceptable in Spanish society for someone named Jesus while in the rest of Europe such as in England the name Jesus continued to be considered to sacred to be used as a regular person's name.