It's my name and I've always absolutely hated it, because it's the most commonplace female name ever, and, really, the default girls name, (I'm a reader, and whenever there's an example female to illustrate a point in a non fiction book, she's almost always a Mary ...) A name is a description, and, who wants to be described as any typical person someone might meet on the street - or, as a grain of sand on the beach? Which is what it feels like to me to be named Mary. I had psychological issues about that by the time I was in my teens. I honestly don't think it matters that there's been less Marys for a while, because it's been so overused - if you got a pound for every real or fictional Mary you could find within the books in a library, you could probably buy yourself a house! - and I think it still has that conformist, undistinguished, sheep image to it.
It's also a huge one with Catholics, and has got me a lot of negative attention from deeply religious Catholic males obsessedly looking for someone like the holy madonna and, especially, a virgin, (seriously!). If you're not a Catholic, I think you need to be aware of that - that Catholics idea of who Mary is and what Mary means might be something you're profoundly unaware of, and yet your daughter may be having that projected upon her by Catholic people, including romantically, when she grows up. It's heavy stuff.
I just wouldn't use it, honestly. Too many people hate it so your daughter has a good chance of hating it too.