Lady Gaga has always been a huge supporter of The Muppets, and her wearing the Kermit Coat was one of the "Significant Events" that I believe helped propel them back into the public eye. She has also appeared with Kermit (or at least a form of him), Miss Piggy has covered one of her songs and parodied her coat, Gaga quoted Kermit as being "her whimsy" in an article about the things that inspire her, she discussed the use of Kermit-as-fashion in a response to Peta and she holds many of the same values as The Muppets.
Which is why, if she named him after Fozzie, it was an honour. And why we should refer to her as Lady Gaga.
Also, Lady Gaga is her performance art...not her reality.