Preparing for an Interview
"Anonymous" means the reporter can quote you directly, but not use your name.
If you want to say something to a reporter, but don't want your name used, you must clearly indicate that, and make sure the reporter agrees to it before you open your mouth.
If using your name is a deal-breaker, make sure the reporter understands that, too. Many reporters these days will not use anonymous sources. There are many potential hazards, and frankly, it makes readers doubt the veracity of someone's information if they aren't willing to give their name.
Off the Record
Generally, it's safest to assume there's really no such thing as "off the record." If there's something you don't want to see publicized, don't share that information with a reporter or anyone else connected with the media, on or off the record.
"Off the record " means the information you are giving the reporter cannot be attributed to you in print or in conversation. However, that doesn't mean the reporter cannot try and verify the information somewhere else. If that verification comes, the reporter can use the information in his or her story. Remember that in trying to verify the information, the reporter will have to repeat the information – that could lead to someone guessing or assuming it was you who gave it out. You cannot go off the record retroactively.
The best way to make sure that what you say off the record remains that way is to have a discussion before the interview starts about the reporter's understanding of "off the record." Make sure the two of you are on the same page and that the rules are clear. If you want to give a whole interview off the record, you must clearly indicate that, and make sure the reporter agrees to accept the information you are giving.
If you want to say something "off the record " in the midst of an interview that is on the record, you must also clearly indicate when you're going off the record and when you're back on the record.