hun, i am glad they are changing the middle name and i think it is a little odd to have both the first & middle names the same especially when they know it's exactly the same as your DD.
However when i was younger my dad had a very close friend (my godfather) who also named his daughter L (i was born first), iw as given my mums middle name as a middle name but it also had meaning to them as a family (although at the time my mum didn't know that), in the end they decided against it (as i was already named that) but to this day we joke that i am his L.M

If she has done it as an attention thing i think it's so so wrong, if they loved both names and it DID have significant meaning to them then i still find it a little odd but we all have our reasons for choosing our babies names, who is anyone else to decide why we can't use a particular name?
I'm not downplaying your feelings at all, i completely understand why it would be so frustrating (i'd be annoyed if it happened to me) but i think it comes down to personal choice, if they want to confuse everyone and make it hard for themselves then i say play it up.. take it as a compliment and brush it off.... but you don't have to worry, they are changing the name now