There's a scene in the 2011 film Thor in which the characters come across a book about Thor, the Bifrost, and so on. The page about Thor has the following words in large, bold letters:
THURSDAY - THOR'S DAY
The characters share their findings and research with each other several occasions throughout the film, so it's possible that either Thor had a chance to look at this book or someone mentioned the information to him.
Thor and his friends seem to have a decent understanding of how their previous visits to Earth have impacted humanity.
FANDRAL: This isn't like a journey to Earth, where you summon a little lightning and thunder and the mortals worship you as a god. - Thor (2011)
Thor is aware that his previous visits to Earth have impacted history and civilization. Given that he knows some humans worshiped him as a deity, it seems very likely that he would also be aware that Thursday was named after him.