One of the several reasons your trademark might be refused registration by the USPTO is that your proposed mark is scandalous or immoral. Without too much further explanation you might guess that a certain word starting with “F” and rhyming with “duck” might be problematic as a trademark. You would be right. Trademarks can be refused registration for being scandalous or immoral. Now you might think that this is America and you can say what the F— you want, and you can. But at least for now, you aren’t going to get the US government to help you protect that as a brand name.
But many people do try anyway. In fact, if you search the USPTO for applications for marks containing that word, you will see nothing but refusals (were 0 for 53 so far), probably causing the applicants to shout . . .