Will it my charges be dismissed?

Okay, here is the thing you need to worry about. When they asked you what your name was, you should have told them. You have to identify yourself when asked. Drunk in public, not to worry, you were in your home not in public. The search of your home was illegal. They have to have probable cause, a warrant, or your permission. Meranda might cover you on not giving your name because you were in your home.