Do you have to change your surname when you convert to Judaism? And what is the meaning of changing your name?

Shalom! You definitely don't have to change your family name, just as many Jews from birth have a variety of last names, from languages of all of the different exiles, including Yiddish, German, Russian, Arabic etc. Nevertheless, of course it would be commendable and a nice idea to choose a Hebrew last name to feel and be seen just like any other Jew, and to be proud of your newly chosen people. Many rabbis actually Hebraicized their names upon making aliya to the Land of Israel, to feel that much more Jewish (like Rabbis Neria, Yisraeli, Goren, Yashar, Ra’anan, and many more), as I did myself (from Chwat to Shvat)! As you probably are aware, the halachic name for aliyot to the Torah, ketuva for marriage etc., will be Ben-Avraham, the son of Avraham. With Love of Israel, Rav Ari Shvat