Do you have to have a Muslim name to be Muslim or not? Because my friend is a convert but she doesn’t have a Muslim name, her name is Payton.

It is not a requirement for a Muslim to have Arabic, Persian or other language names, as long as her given name does not represent shirk (like the name Diana - goddess of love) or have a bad meaning. Hence she may keep her given name without changing it.

Family names should not be changed under any circumstance because Allah (swt) said: “Call them by [the names of] their fathers; it is more just in the sight of Allah “.[1]

Reference:

[1]  (Al-Ahzaab: V 5)