Your mother is a fucking bitch.
Do you know what she's doing? Now that you have a baby, she's pissing on what she sees as the new, revised boundaries of her territory - your motherhood, your new family, your baby.
You ain't gonna get to be the big grown-up mum, who now isn't the 'kid' any more, and has her own baby that she gets to set the rules for. Oh no. You're still the subordinate. She is the boss, and that includes how your baby fits in to the family. She is showing you that you don't get to call the shots with him.
Lots of narcissistic mothers are like this. They cannot BEAR the focus shifting when a baby comes along. They can't bear the baby being the new focus and worse, them not being the mum of said baby and therefore at the centre and the 'boss' of the baby stuff. They have to pour in a bit of scorn and try and put you back in your place. You ain't mum. She is.
The absolute only way to deal with this is zero tolerance. You need to set the boundary and it needs to be cast-iron, because this is only the start of it. The sooner you do it, the better it will be.
I assume you're not seeing her face to face. Next time, put the phone down. Immediately. She'll call back. You say 'Sorry about that. I'm not prepared to hear you call my son, your grandson, the wrong name any more. I know you know his name, USE IT or let's just not speak.'
She goes bananas. You slam the phone down again.
You will, if you can hold your nerve, get away with this because everything has changed, and YOU are now the mum with the baby and actually, she can rant all she likes but if you hint that you will stay away, she'll shit her pants. If she gets the impression from you that yes, you're mum, you're damn well going to inhabit that space and you will pull rank... she will back down.
Her fear is that you will do this, she knows you have the whip hand now as mum, so she's trying to batten things down almost before you've found your feet. Fight back now in a controlled way - phone down - do you need to see a doctor mum? - No, I won't call, it's upsetting and makes us very angry to hear you calling our son the wrong name, looks like we might have to wait a while before we're back in touch until you can learn his name, eh?'