I grew up with a Welsh name in England. I was in my late 20s before I met another person with my name and have yet to meet a 3rd. I like it that way and wouldn't want my child to have a very popular name.
I wouldn't name my child a name I didn't like, but I have a few naming criteria such as not too popular, not starting with the letters C, G or H, bonus points if starting with E as it's my favourite letter and preferably Welsh! I like the letters A, E, L, M, T and S.
There are a few top 100 names I've always liked, such as Isabel, Isabella and Lucy, but I wouldn't use them as I want something more unusual, ideally Welsh like Eira, Eleri, Tesni or Morwenna. I wouldn't rule out popular Welsh names in Wales such as Osian and Seren. I would also consider the Welsh versions of top 100 names like Tomos, Alys and Nansi. I'd also consider non Welsh names like Lyra (albeit relatively popular), Juliette and Iseult.
Fortunately there are a huge range of name options between Sophie and Tinkerbell and lots of lovely but not so commonly used names. There's a difference between unusual and 'youneeq'.