I enjoy Tulips. They happen to be one of my favorite flowers, if not my #1. However, I don't think it works as a name at all. There's a reason why it isn't commonly used.
A classic, more standard name would be best with it such as
Jane, help balance out the weird.
Other ideas:
Tulip
Alexandra Tulip
GwendolynTulip
DelilahTulip
MaeTulip
Josephine