In the movie watchmen one of my friends said the blue guy is like always naked is this true?

Yes he is. When in public he wears clothes. The reason he's naked is that 1. he spends most of his time at a nuclear facility performing tests on himself and 2. He can grow to the size of a giant or large building when he needs to and there aren't really any clothes made for that. It's like The Hulk- the moment he grows his clothes are ripped apart.