Forget what your mother told you about evil thieves stealing one dollar bills out of mail boxes. However, many people publish zines under pseudonyms. Unless available only for a ridiculous amount of money, just send cash. Be warned about a few things. There are no guarantees.
Checks are likely to be thrown away.
If the name of the zine is apt to offend your third-grade teacher, don't put it on the envelope. Some zines published in rather provincial parts of the world won't get their mail if the publisher's name isn't on the envelope, so whatever the name is in address, that's the name that should go on the envelope. We can work only with what information is provided to us. We'll post any special requirements that are conveyed to us. If a zine is free, you may want to help out with some stamps.