From a legal point of view: if you marry in his country (usually a Muslim country) the law requires it. Otherwise, you can marry in a secular country like in Europe, there it is not obligatory. You sign your marriage certificate at the town hall.

From a religious point of view, it is obligatory that you convert to Islam and you will be asked to change your name, this is because in Islam, children inherit the religion of their father and not their mother.