Originally posted by Jmanghannever by name no. He says that he fought somebody that looked exactly like Goku and that it was his father.
Does Frieza mention Bardock by name? By word? Cause if not, then no, Goku has no idea who Bardock is.
I think vegeta tells goku about his father in the saiyan saga though. He discovers how to turn into the great ape without the moon.
http://www.goodmanga.net/dragon_ball/chapter/307/7
Frieza didn't say it out loud. It just thought it to himself. He never said to Goku period that he killed his father or at least in the Manga. Vegeta never mentioned Bardock to Goku either. The poor English dub had Vegeta talking about Goku dad was a average fighter but a amazing scientist. But as I said that never took place in the Manga or Japanese version of the Anime.
So in canon Goku doesn't know anything about his dad. But I am assuming if he found his dad did care about him and so did his mom Goku still wouldn't really care.