Should I tell my girlfriend to stop talking to this girl?
Wait, why would you want your girlfriend to stop talking to her?
My partner doesn't have many friends and I like it that way.
You should not try to keep your partner from having a social life. If you do they will resent you for it later on.
I want her to never grow close to anyone else.
Wanting her attention is fine but wanting to monopolize her is wrong and very controlling of you. She will end up resenting you for that in the future and you need to learn to let her have her own life separate from you. It will do you both some good.