Are any of the names your favourite?
My whole family know I love Edward down to Teddy. Personally I would be really upset if they named their child Teddy, as have pretty much been set on it since I was really young and have let them know.
So I guess she can say - yeh I really want this name. If it isn’t one you really like then why would you choose it anyway?
Of the people with huge fall outs because of names - I personally wouldn’t do that. I’d be pissed if it was Teddy. That said - I would actually still name my child it (unless literally a niece and nephew - then I’d enjoy them having the name).
My mum had her boy and girl names picked out. After 2 boys, my aunt used her girl names for first and middle of my cousin. My mum then had me and was pretty annoyed - but was thankful she had other names she liked and kept her annoyance to herself. However, when my dads cousin used my name for her daughter (born about 9 months later), it did annoy my mum a lot more - though didn’t impact their relationship.
So summary - if she has one die hard name and it’s not a favourite for you, I wouldn’t use it whether she is single or not. Otherwise keep it to a middle name.
If she’s given a list of 5, and you like one. I’d phone and say can I use this - or is there one name which is your 100% favourite. What’s the chance she has five kids?
If you end up with cousins with the same name, that’s life. But if your husband is backing her, there might be more to the story than you realise. Some people (myself included) have had favourite baby names from very young and there is no reason to use one unless you are 100% set on it - that said I think vetoing five is quite extreme. I have about 5 boy names and 3 girl names I would have on my shirt list - but only 1 I would actively be upset about.