Despite being the "player character" Frisk is their own character, as it's revealed in the end of Pacifist route,when they are talking to Asriel.

Despite that though,there is a lot we don't know a lot about Frisk as a character, in game filled with colorful personalities. It doesn't help they Frisk has the blankets expression, despite what other characters say otherwise.But we can deduce what type of personality they have by scraping what we got, via the options you pick in certain situations their in, or through dialogue.

For example when "battling" against the Royal guards dogs, you have the option to pet, and play with the dogs, and when you pick those options, the text explains how Frisk is doing them, and they seem to have a lot of fun, playing and petting with the dogs, so we can assume that Frisk is a dog lover. There's even at one point, in the game. I dont remember where, but I think it's at the True lab where you are up against an Amalgamate dog, and when given the option to play with it, the text mentions how Frisk is "laughing and laughing hard. or something like that, I can't be too sure correct me if I'm wrong.

When going up against Undyne, she calls you a "Goodie Two Shoes," and calls your additude Saccharine, which implies that Frisk is a very sweet kid.

I know this is not a personality trait, but the game also implies that Frisk is not a soda fan.

But that's just my two cents, I could be over analyzing it though.

I think Pacifst is the closest we get to knowing Frisks personality