Yes. It's a marketing ploy to simplify their brand into the most frequently used word in the English language, that is also only 3 letters in length and will fit in big letters on a hat. They want to be able to sell hats and shirts in their scarlet and gray colors that just say "THE"... and have everyone immediately recognize who it is referring to.
It makes good sense from a marketing perspective, except that it is so pretentious of them, that it could backfire. You don't want your brand to be associated with silly, arrogant behavior that everyone else ridicules... and this will make them the butt of jokes, for sure. It already has.
Yes, he did in 2013. I think he was successful though.
In Manziel’s case there was also partially an issue of another party - an organization called Kenneth R. Reynolds Family Investments, based in College Station, Texas - filing for the "Johnny Football” trademark in 2012 on their own (presumably for profit and merchandising).