Grandmother often refers to herself as "Mom"

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

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!

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.

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

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

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.

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.

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.

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.

Yes have a chat with her.

As a new gran, even before my granddaughter was born I was negotiating who gets called what with other gran, who already had grandchildren.
My own Mil did the same, but a year in, decided she wanted to be called something different as my kids' cousins (Who are younger) had started to call her something else. We just carried on calling her what we had always called her,
Keep it simple. Talk to her saying it's confusing.

JackyB, she has been given a special name - Granny.

Def a gran but love mumsnet!!!

Sounds like the beginning of dementia - maybe she slipping back into the past ......

I didn't really need a special name, I'm Granny, other GM is Nana, both our own choices. The DD read an article about names for GMs.
We all decided on ELderly RELative but it only really gets used on here! My friend Barbara is Baba to her, now teenaged, GC and is very happy with it.
I do forget I'm actually a GGM as of a few months. I mutter to myself 'I am NOT her GM, she has two GMs already!' My own GM told my DD to call her Greatie which worked well.

The should be TheN ?

Would never call myself Mum to my grandchildren even though I have been known to lose ones marbles on occasion but then I love being Nana and have for the last 11 years also I am only early 50s so dont think its an age thing.

I've spent so many years calling myself "Mummy" or "Mum" to my kids that I quite often get confused when talking to my DGC. My family know that I never get their names right so they know I don't mean anything by it. I doubt it is meant offensively by your MIL, she's probably having a senior moment.

I would correct her every time. I find her actions rude and demeaning to the real mum.

My youngest granddaughter called me 'Mumma' for a while when first learning to talk. Although she always called her mum as mummy. She's now 4 and calls me grandma. I don't see the problem unless it's a deliberate action by the grandmother, or unless she's confused? In which case some understanding would, I am sure be appreciated.

Why on earth would a grandmother want to be called mummy/mommy in the first place?

Possibly she didn't like being a mother to her own child and likes yours better.
DGD once announced to me arriving for a long stay that she might well call me mummy by accident. I replied that it was very kind of her to think of me like that but she couldn't be sure of getting a response as I was programmed to answer to Gmaman. I think she was fed up with her mum at the time.

Put a stop to it now - this may be only the beginning - she may attempt to undermine your authority as the children grow and you should tell her not to refer to herself in that way. Yes it is confusing for the children, but let's be honest, in calling herself Mum, she's saying something about the relationship she wants with them, and not about what's in their best interests. You don't request her not to do this - you tell her it's unacceptable.

Smile, nod, ignore.

Eh? She's not talking to the OP, she's talking to the children....and I don't really think 'ignoring' is the answer in any case.