Legal Question in Intellectual Property in Alabama

Your use of the term "The Dirty Dogs" began the process of what's called a "common law trademark" even though you have not officially registered it. Using that name on iTunes most likely staked your claim to that term to the U.S., if not globally. If you do not send a demand letter to them claiming your rights in the name you may be giving up your rights in that name by what is called "estoppel."

Prepending a "the" to the front of the name is likely immaterial. Consumer confusion is the heart of trademark laws, not grammar technicalities. There are two main types of trademark lawsuits - Direct Trademark Infringement and Trademark Dilution - and they each can result in an injunction. Your scenario would likely qualify for both grounds, but as I mentioned before you should send them a registered demand letter immediately or else they may claim you gave up your rights through your failure to act. There are probably templates for such a demand letter on the internet; however, an attorney should likely be consulted as such a letter will be admissible evidence in any future court case.