Baby names

I'm due with my first at the end of November and my sister-in-law is due a week behind me with her second. We were having a nice BBQ today and we're talking about baby names. Both of us not wanting to tell. So we just said the first letter of the names we have picked. It turns out that our girl names are pretty much the same. We have chosen Lillian (Lily for short) and them Lilyana. We have both chosen the root name Lily as that was my husban and his brothers late grandmas name. 
Should we start looking for another name? As they aren't changing their name, they made that very clear. I don't want to feel like we gave in as I still love the name but don't want them having the same-ish name. I should also point out neither of us are finding out the sex so this may not be a problem...