I've got a photocopy of the actual Registration of Death Record, it's all handwritten by the doctor. That's about the only info I have on her.
In the spot where it says father's name, it just says Braw, that's where I got that from. I'm looking at it right now, and I'm pretty sure it's a W at the end. It says she was a housewife, and the doctor's W on housewife looks just like the one at the end of the name, so I'm pretty sure it does say Braw.
The weird thing is, in the two censuses that I found for her (from 1906 and 1916), where I'm sure that it's actually her, one says that she was born in Ontario, Canada, and the other says she was born in England. So I'm not sure if Wales is even right, maybe she was from England.
The unfortunate thing is, I really don't have much info from my family. Mary Ellen died when my grandfather was 4, so he didn't know her, and he actually died the same year I was born, so I never had a chance to talk to him about any of this.
My grandmother says he never really talked about his parents much, so she hasn't been able to tell me much about them either.
The death record came from a researcher that I got in touch with in Weyburn, Saskatchewan, where Mary Ellen died. She sent me some information, although most of it is about Mary's husband, William McDermid.
I want to thank you guys for your help. I know that it's hard to come up with much when I don't have a whole lot of information to go by, but the main thing I wanted to see was if Braw was a common name in Wales. Since it doesn't sound like it is, I'm thinking there's been a mistake somewhere, either in the surname, or about her being born in Wales.