Bryn Price. It wouldn't be hard for an internet stalker to find out my full name, so I might as well give it.
It's a Welsh name, though my family's not Welsh, nor do we live in Wales, I was just born in Wales and hence I received a Welsh name.
Well, "Price" is generally a Welsh name too, so there must be some in your ancestry. It's a form of Ap (son of) Rhys. Or, at least, that's what I read somewhere. I'm not Welsh either. I'm Polish, and my name is Ivona.
Price has other origins, but you are correct. Price can be English as well, the blood in my family is English, Irish and Greek, but as far as I am aware no Welsh, though my aunt did marry a Welsh bloke, but if that makes me Welsh, it also makes me Sri Lankan and Indonesian.
(as I have aunts of each nationality)
Also, Bryn can be Scandinavian too, usually derived from Brynhilda, but normally it's a girl's name, in Welsh however, it's a guy's name and it means 'hill', so it doesn't really mean anything interesting.