Why are characters called Champions rather than Legends?

Better than calling them all Heroes.

I'd assume it's because they are champions and as the lore is unfolding there is quite a legend surrounding their backstories.

They are Champions of Runeterra. The things they do is what will make them Legends.

Because lore wise, each of us is a Summoner that is put into this sort of match to see which team of Summoners can prevail. Now what do we do as Summoners? We pick a character to fight for us in our name instead of going down to the Rift ourselves, also known as having a Champion to fight for us.

Its because of the old lore that was retconned. Also it was orginally called league of legends clash of fate but they dropped the end.