Can i trademark a beer name that used by another brewery in my state? They don''t have the trademark and my beer is different.

As a general matter, "trademark" is a noun, not a verb. In other words, you do not "trademark" a name; you either have a trademark or you don't by virtue of having used the name in commerce. Also as a general matter, the prior ("senior") user of a mark has the right to use the mark and to exclude a newcomer ("junior" user) from use of the mark. This is the result whether or not the senior user has registered the mark. Since the two beers are similar, the senior user's mark -- if it indeed functions as a trademark -- would be infringed by your use. There are additional problems with the fact pattern you put forth. It is possible that the term "purple porter" doesn't function as a trademark at all, but is, as is said in trademark parlance, "merely descriptive" of the product. If that is so, then it cannot function as a trademark for either the senior or junior user. As an example, the term "red car" or "blue auto" could not function as a trademark as applied to automobiles. It is not clear from your inquiry whether your product is, in fact, a porter beer that is colored purple. If so, you would likely be free to call it by its generic name.