Yehoshua was the proper Hebrew name, but Yeshua was the common Aramaic name.

For one reason, he was only Yehoshua in the synagogue where Hebrew was spoken. In the commons he spoke Aramaic and was called Yeshua, which is still used by millions of covenant Christians (of both Jewish and Gentile races). The rest don't bother to learn the names he called himself in his local languages, just as they don't know who Kong Qiu was ("Confucius"). Both Jesus and Joshua descended from the Hebrew roots, and are recognized as the same name without either being more "wrong" than the other; the KJV also refers to Joshua ben Nun as "Jesus", for instance.

Since I'll need to comment on OP sooner or later, Yeshu was a common Galilean-dialect nickname for any Yehoshua; it does not remove the savior meaning any more than "Jack" removes the gracious meaning of John (it's still there, just not in focus). The Talmud includes three people who got nicknamed Yeshu: Yeshu the Student (2nd century BC), Yeshua of Netzeret (1st century AD), and Yeshu ben Pappos (2nd century AD). There are also passages about "Yeshu" as a stock backwater character without reference to which if any historical Yeshu is intended. Therefore the actual status of the Talmud is that most Yeshu passages either are anachronistic with Yeshua or leave it to the reader to decide which Yeshu is intended (allowing many readers to apply them to Yeshua); and there's really only one passage that is clearly about Yeshua of Netzeret, and it's pretty mild by comparison, giving an important confirmation of his trial, his Passover execution, and his martyred disciples. The blasphemy is not in the text but only in the cultural context, such as when it says Rabbi Ulla blasphemed Yeshua. OP combines a number of justified statements with a number of unsubstantiated leaps, and I don't always watch his videos (sometimes relying heavily on AI) to try to sift which is which.

And all this time I was saying Hey, Zeus!