Why is Alan Moore's name not shown on the Watchmen credits?

He didn't want to be credited.

From a Guardian article:

Moore has a complicated relationship with money. "Pure voodoo," he says now. "Only there as long as we believe in it." Challenged, during a television interview this year, about why he would sign away the movie rights to a comic such as Watchmen if he didn't ever want it to become a movie, Moore said he gave up the rights because he never expected any adaptations to happen; he called it making money for old rope. But then the films came out, and somewhere along the way Moore developed such a distaste for what he saw on the screen, and the revenue accrued from it, that he asked for his name to be taken off the credits; then he started turning down production money. Moore gave his share of the Watchmen fee to Dave Gibbons, the artist with whom he conceived the series.

His Wikipedia page goes into surprisingly good detail on his views on this. The page includes a summary of an article on Comic Reporter, stating:

Moore has subsequently stated that he wishes his name to be removed from all comic work that he does not own, including Watchmen and V for Vendetta, much as unhappy film directors often choose to have their names removed and be credited as "Alan Smithee". He also announced that he would not allow his name to be used in any future film adaptations of works he does not own, nor would he accept any money from such adaptations.

So effectively, he just doesn't want to accept any finance from it as he's not happy with the film adaptions of his work.

To quote one final article (from Left Lion):

You’ve always refused to put your name to film adaptions of your work. I know this is going to be hard to put a figure on, but how much money do you think you’ve turned down, for taking a moral standpoint on this?

Well, they asked me if they could give me a huge amount of money to bring out these Watchmen prequel comics – which they were going to do anyway - and that was probably a couple of million dollars. I should imagine with all of the films it would be another few million? In a way it’s really empowering to do that.

You can’t buy that kind of empowerment. To just know that as far as you are aware, you have not got a price; that there is not an amount of money large enough to make you compromise even a tiny bit of principle that, as it turned out, would make no practical difference anyway. I’d advise everyone to do it, otherwise you’re going to end up mastered by money and that’s not a thing you want ruling your life. Money’s fine if it enables you to enjoy your life and to be useful to other people. But as something that is a means to an end, no, it’s useless.

It's also worth noting that both Paul Levitz, president and publisher of DC, and David Lloyd, the V for Vendetta illustrator, found it difficult to sympathise with him. From the NY Times:

Mr. Levitz said that such so-called reversion clauses routinely appear in comic book contracts, and that DC has honored all of its obligations to Mr. Moore. "I don't think Alan was dissatisfied at the time," Mr. Levitz said. "I think he was dissatisfied several years later."

Mr. Lloyd, the illustrator of "V for Vendetta," also found it difficult to sympathize with Mr. Moore's protests. When he and Mr. Moore sold their film rights to the graphic novel, Mr. Lloyd said: "We didn't do it innocently. Neither myself nor Alan thought we were signing it over to a board of trustees who would look after it like it was the Dead Sea Scrolls."

Alan Moore is notorious for refusing to accept credits, for what he considers to be the 'poor taste' of the output produced.

Moore has a complicated relationship with money. "Pure voodoo," he says now. "Only there as long as we believe in it." Challenged, during a television interview this year, about why he would sign away the movie rights to a comic such as Watchmen if he didn't ever want it to become a movie, Moore said he gave up the rights because he never expected any adaptations to happen; he called it making money for old rope. But then the films came out, and somewhere along the way Moore developed such a distaste for what he saw on the screen, and the revenue accrued from it, that he asked for his name to be taken off the credits; then he started turning down production money. Moore gave his share of the Watchmen fee to Dave Gibbons, the artist with whom he conceived the series.

The Wikipedia article on the movie has quite a definite answer on it:

Dave Gibbons became an adviser on Snyder's film, but Moore has refused to have his name attached to any film adaptations of his work. Moore has stated he has no interest in seeing Snyder's adaptation; he told Entertainment Weekly in 2008, "There are things that we did with Watchmen that could only work in a comic, and were indeed designed to show off things that other media can't." While Moore believes that David Hayter's screenplay was "as close as I could imagine anyone getting to Watchmen," he asserted he did not intend to see the film if it were made.