Do you have to pay company’s money for saying their name in a song? Or...?

Not always...this depends on the company and if an agreement was reached before the song was produced. Weird Al's staff normally gets the approval on using companies names and other people's songs before he produces them (only 1 that I know of didn't have actual approval, and the artist was pissed, not sure what happened or why). Yes, it is freedom of speech, so technically, they don't have to pay or get approval, so it just depends on the company (ie=verizon isn't going to pay Nextel, its freedom of speech, although weird Al gets approval to make people happy).