Not More Names but New Names.
A thing often lost in western cultures compared to other cultures is that names often have very specific and important meanings.
In America we name our children things like Jacob because it sounds nice when you say it with the child's intended last name.
However in Hebrew the name Ya'aqov (the non-anglicized version) means "to follow after" because Jacob was literally a second son. He was meant to dutifully follow his older brother. It would be the equivalent of an American parent naming their child something like Dutiful. It clearly has meaning to the parents and exemplifies what they hoped their child would be.
However what happened later is that Jacob ended up deceiving his blind father Isaac into granting his blessing onto Jacob instead of his elder brother Esau from there he travels outside his home to Haran and has a series of visions and enounters that he struggles with before deciding to return home.
Enroute to home to go to the funeral of his father Isaac he ends up in a fight with a man or angel (different sources are inconsistent) and the one he fights identifies himself only as God. At the end of the night after Jacob is badly hurt but still survives at dawn he asks for peace and the one he fights gives it to him asking his name.
When Jacob replies with his name the one he fight renames him as Yisa'el or "one who prevails with God" this name in modern translations is Israel and where the nation gets its name.
This is often derived as literal but it also can be figurative because Jacob/Israel often struggled with his duty to God and after this time he came into his inheritance and became the leader of the tribe as a whole. It is as much about his growth as an individual as his accomplishments.
The giving of a new name strongly says this is no longer the man you knew he is a new man.
It was commonly done when a foreigner earned a place of trust in foreign land. Give them a domestic name with a meaning.
If you hunt down a monster that plagues the norse kings house and secure his throne he is likely to trust you even if you are a strange frankishman. Give them a good Norse name depicting their role they had. Tales won't be told of the Frankish man Nadalfried they will be told of Skjold. They are the same person but also not. It is as much about national dignity as about the person. You can't have a foreigner saving your nation and so the names in the tales will be of a local. Even though he isn't one.
I would strongly recommend to give out many names to players and have them go by them across nations. Have it be what people call them in different lands. It is earned.