I was doing some searching today while waiting for a phone call. I looked up the name Alizee. in the white pages. I had to use it in the last name block. I thought it probably wasn't just a coinicidence that 3 of first names that came up would have put them being born when Alizee was at the height of her popularity.
Two other names though belong to people at least 40, so though it "might" have been rare as a first name, it certainly wasn't unheard of and apparently there must have been quite a few people around with a last name of Alizee.