I agree with what tinymeteor said up thread - teaching the children to demote an adult in their life by calling them their first name, is passing the adults issues onto the child.
I understand that lots of people have very complicated pasts. Their relationships with their parents and step parents or parents new partners are not always easy. If a parents partner is new or likely short term, then I get why using the name 'grandad' or whatever might not be right.
However, if that adult is a permanant fixture, then they will be part of the child's life for many years. I think most of us would agree that having more older, interested and loving adults in our child's life is a good thing. One poster said that this adult would never ever be called Grandad by their children - well to me, that sounds controlling and dictatorial. It could well be that the children develop a great relationship with this man who is married to their Granny and absolutely want to call him Grandad - and really it isn't then up to the parents to choose.
I think that when people go through these thought processes when pregnant, they are really thinking about themselves and not their child. They do t want to call the new partner Dad. That is absolutely fine, because it is about their relationship with this person. They forget when thinking theoretically about all this, what small children are like and how issues of the past and technicalities mean absolutely nothing to them, but what does matter is the people who are actually in their lives and who play a loving role in their lives. They will call this man whatever word they can get out of their mouth as they learn to speak. They will call him a name without it having any connotations or baggage attached to it. And why would an adult want to add connotations or baggage to what is an innocent and unsullied relationship? Why would an adult need to force the child to demote this adult in their eyes and the world, unless it is to purposely hurt them or their mother who has married them.
OP, your mother has married this man. He is there to stay and if you can find it within yourself to be generous at this point and open handed and inclusive towards him, you will do all kinds of favours to your relationship with both your mother and him. I always remain surprIsed at how reluctant people are to build bridges, but how quick mumsnet sees are to suggest actions which will widen gulfs and how a lot of this seems to come down to power.
OP I can see has an issue with someone else telling her what this man should be called and it is a big deal to her that she should choose as the mother of the baby. This is about asserting power and control. PErhaps OP could consider if it is really necessary to do this and to assert control over this. Is it a matter that really needs this and are the consequences worth it for a bit of saying 'my child, my choice'. In my mind, the big, generous thing would be to allow a special name for this man. A bit of a discussion with The family might be in order. All families having a child need to decide what the various grandparents will be called - and it can be a source of limited tension when even only natural grandparents are involved. At the end of the day, it will be up to OP to manage the discussions, especially if 2 people would like the same name. However, I think the really important thing in all this is that all the adults are treated sensitively and feel they are listened to and welcomed into the babies life. OP are you able to have those discussions, be sensitive to all the adults and most importantly, to genuinely welcome all of these adults into your babies life?