What do you guys think of the existence of two characters with the same name?

Ya see, as soon as I found this forum, I couldn't help but start thinking about what sort of character I would want to play here. I came up with the name Hana Wu, which I think is a good solid earthbender name, and I started building from there. I have since started falling in love with the character (as I tend to do), and thus with the name as I feel it suits her very well.

However, as I’m sure you know already and as I soon discovered, someone else also thinks that Hana is a good earthbender name! I understand that same names can potentially cause confusion, and the lack of diversity might seem unappealing- but it is realistic. Maybe Hana is a popular earthbender name?

I, of course, would want to ask Itsune Kokejin what she thinks of the matter as well; I wouldn’t want her to feel as if I’m somehow infringing on her rights to her unique character. But I thought I’d run this by you guys first to see if it might be too irksome to have two character with the same name. If this doesn't fly for whatever reason, I'll just get back to the drawing board and deliberate to find another suitable name.