Hi, I guess its adj. is gossipy. I didn't find gossip as an adjective in the dictionaries.

"Gossipy" is the adjective. For "Gossip Girl", it's merely a descriptive term but not necessarily an adjective, same as "United Nations Ambassador" or "Wal-Mart Employee". Or see it this way: "Ambassador of the United Nations", "Employee of Wal-Mart", "Girl of Gossip". I think you're asking if "gossip" can therefore be applied as an adjective to other words, but this is not so. Use "gossipy".

in american english it can be possible. but in traditional i dont think so

yes, a America serial is called "Gossip Girl" here the gossip is adjective.