Your SIL sounds very insecure. She might act this way to get approval, or she might have a really difficult time making decisions.
As much as it angers you (and I'd be right there with you if I were in the same situation), she does have a right to name her kids whatever she wants. You have the same right and could use the same name. Would it be kind of confusing at family gatherings? Yes. If you love the name(s) enough, though, you'll have to decide if you can live with having two kids with similar names in the family.
Oh and why the heck are you staking out claims on baby names with MIL when you aren't even pregnant yet? I wish I had kept my mouth shut in the first place! End vent.
You're pregnant now. She's presumably not pregnant right now. Your baby will be born long before her next baby is born, so in any case, she can't "steal" your baby name. In the meantime, it's probably best that you and your DH keep baby names to yourselves if you're worried that your SIL will copy your names.
I said I feel like she just lacks her own identity and confidence and have tried to see it as a form of flattery.
I would agree. She probably is really looking for approval and acceptance and really doesn't know how to make decisions with any confidence. What I'd do in this situation is keep any plans for the future (vacations, baby names) vague, and if she presses you for details, tell her that nothing has been finalized. Maybe you could even offer to help her pick out her own vacations and/or baby names to help her gain some confidence.