Baby nickname after I said no

So my MIL keeps trying to give my baby a nickname. She has said it more than once even after I said I am not giving her a nickname until she’s old enough to know her name. She said she refers to my LO by the nickname she’s given her to all her friends and other family.

Is it a big deal? Am I over reacting?

I always just tell her I want her to know her own name first so no I’m not calling her by anything other than her name.