Name-changed for this as, to be honest, I don't think I'm going to come out of it well 
- but I have to ask...
After much thought and deliberation, DH and I named DS 'Jake' (names have been changed to protect the innocent). MIL insists on calling him 'Jakey', which I find incredibly irritating (DH doesn't really care, but is trying to support me!). We have asked her nicely not to refer to DS as such, but rather than backing down and just mumbling something about having a miserable DIL, she's pushing back, wanting to know WHY she can't call him that, he's her DGS, etc.
I completely get that in the course of his life, DS will probably pick up all sorts of nicknames and I will have zero control over it, but for now he's not even a year old! But - before you tar me completely with the 'one of those mums' brush - it's 'Jakey' in particular I cannot stand; we've said to MIL she is welcome to call him whatever other pet name she bloody well wants. Also, I know another baby who's actually called 'Jakey' - as per birth certificate, not just a nickname. So to me it's a different name altogether. Like if I called my child Bob, but MIL insists on referring to him as Dave 
If DS wants to go by 'Jakey' in future and sound like an utter twat then I will absolutely suck it up and cope.
So, AIBU or is MIL?
ducks to avoid deluge of biscuits