Islam ensure that all his followers' safety is protected. Through Allah Almighty's sayings in Quran and Prophet Muhammad (Peace be upon him ) actions, it is made clear to Muslims what to do in life and whatnot, in order to save them from all the harms in life and hereafter. Even the prohibitions in Islam have been proved by Science as well. When it comes to the name of a person, Allah has guided humans through a set of rules for how Islamic names must be kept. They should have a good meaning, not the bad origin, the names must be well researched and they should be positive as well. To give a better reference, prophet Muhammad (peace be upon him ) used to keep good names and when he used to hear Muslim baby names, that he did not find right, he used to change them and keep good Muslim baby names. He also changes the name of his wives for whom they did not find right.
In Islam, there are many people who convert towards it because it is the ultimate religion and the religion of peace. But Allah Almighty has never kept it an obligation to do so because it is something they have kept for all their lives and it is also a part to their personalities but still if they want to, they sure can do it.
They should pick up Muslim boy names or Muslim girl names that are authentic, from the Quranic resources and are possessing a good meaning.
As we know that we can also keep Non-Quranic names, such names can also be kept but only when they have a positive connotation and they tick all boxes for being a good Popular Muslim Name according to Islam.