Grandmother often refers to herself as "Mom"

Yes have a chat with her.

My DS2 gets confused and always calls me "Mummy" to his daughter. It takes a lot of concentration to get it right!

But in the OP's MiL's case, it sounds quite intentional - either out of some sort of spite or jealousy, or it may be just absent-mindedness.

Perhaps no special name has been agreed on for her and she is not sure whether she's Gran, Granny, Nanna, or Grandma.

Correct her, politely, or humorously, in front of your children. Or make it into gentle humor like "Silly granny, I am mummy" so that the children learn to treat it as a joke and/or an inaccuracy. If you just don't say anything in front of them, then they might well get the wrong attitude about relationships. This I think is a good way even if it does turn out she has the beginnings of dementia and can't help it. It's what your children hear from you, it doesn't matter whether she changes her words or not, it's just important that the children have heard the correct situation from you.

I do it sometimes I'm afraid. Three year old lives with me and his mum and I forget. He laughs and calls me 'silly nanny'. He sometimes calls me mummy but quickly corrects himself. I also call all my three grandsons by the wrong names, including those of my DS and younger brother.
I am otherwise quite sane.

Jefm - perhaps damewithaname is in America but calling your mother Mom/Mommy is also the norm in Staffordshire and other areas of the West Midlands.

You could try adding "Granny" to the end of every statement you make damewithaname not suggesting it will stop her but you could have some fun with it!
You know "How are you Granny? Would you like a cup of tea Granny? Take this to Granny? Is Granny OK? etc

Sometimes it's assumed when out with my grandsons that I amtheir mum although 60 i probably don't look it so I never correct it as it's quite a nice amusing temporary feeling of lost youth !! The boys call me "mummy I mean Nonna "often ..they get confused. I often have the same maternal instincts as their mother but never would I think that I am or want to be calling myself their mummy

The children know what's what.

It's more than spiteful by the sounds of it; perhaps she missed out on your DH's childhood.

She is known as "Granny".

She in a way laughs it off as "forgetfulness" and then corrects herself BUT like I said it happens far too often to be that way. My 8 yr old does correct her and that's when she laughs it off. She's far from forgetful when it's anything to do with the grandkids though. .. catch my point?

Anyway, I don't make a huge fuss about it but it doesn't sit very well with me.

Thanks again!

ps it wasn't helped by the fact that DS's best friend had the same name as our dog.

that was in response to Ana's post

and yes, mcem my DS got used to being called by the dog's name. It's when you have several children all claiming attention at once that you can get .
I got used to answering when I was called by my brother's name.

such as 'don't be silly Granny, you're not my Mummy'.

Even our 4 year old DGC would probably have giggled and said 'You're not my Mummy, my Mummy is my Mummy and you're my Granny'.

I'm sure all retired teachers here will remember being addressed as 'Mummy' by their pupils. Easy to laugh off.
It's a family joke that we confuse names - mum did, I do and DD does too. I once called out the dog's name when speaking
to my son!
I do think this is different. Has it been the same throughout the life of the 8yr-old?
Have you established a name for her?
What goes in birthday/Christmas cards?
If the name is there just make a clear point of using it often.

You'd think the 8 year old would have said something.

Conversely my GS often calls me 'mummy' ..... I always correct him and say 'grandma' ....a bit of a standing joke now! Then again I often call him 'S' my son's name. I often hear my OH telling him to "ask Mummy" meaning me. I often think these things are a slip of the tongue. I understand your irritation and would just correct her nicely each time! Don't be upset. The relationship between some DILs and MILs can be awkward. You're the Mummy x

Yes, agree that it should be nipped in the bud. You could say something along the lines of "The children are confused about what they should call you - can we think of a nice name instead of 'Mummy'?' Like others have mentioned, my GC often mistakenly call me 'Mummy' but instantly laugh and correct themselves. It looks like MIL is doing it deliberately rather than making a mistake...

My GC used to call their dad, Granddad, by mistake, after they'd gone home from here.

My sister is known as Mum to her grandchildren and their mum in mummy! I have always found it a bit bizarre- so perhaps there's history of this in the family. Is she/you American ( mom/mommy ) or when she talks is she just referring to herself as mom when talking about the kids parents?? It is odd but maybe the question needs asking gently? I cant think that she means harm!!

The GC very occasionally call me Mum when they are with me on their own - I make a joke of it and say : "I'm not Mummy!" In fact my DGD did it just now while I was typing it!

How old is your mum? My mum frequently gets the generations mixed up. Sometimes refers to herself as my DSs mum, sometimes refers to GGCs as her GCs. We just laugh it off. My DSs know who their mum is and my GCs just accept Nanna is a bit forgetful. Never quite sure who she thinks I am when she makes a mistake- her sister possibly I'd just gloss over it. If she's doing it deliberately to annoy you she'll stop it, if it's just a memory slip she'll carry on.

Don't overthink this.
Correct her gently or get the kids to call her "mum's mum" if you like.
Don't sweat the small stuff.

They are 8, 4 and 2.

I could understand saying it by mistake a few times here or there but this seems to be too often to be passed of as a slip up.

Thanks for the all the comments.

Sounds like she's doing it to annoy you. How old are your children?

We don't swear enough for Mumsnet.

My mum did it a few times, I just said in front of my son, 'no I am his mum, you are my mum'.

Mumsnet doesn't offer sound advice. Gransnet seems to offer more constructive advice.