When you go to Renzos put on the white belt. In fact, no matter what your skills are, you should not put on a blue belt, which another black belt hasn't authorized. It is not only dishonest, but it also shows a lack of loyalty and humility. IMO it is ok to put on a belt for tournaments; because, some tournaments won't allow you to compete unless you wear that belt. But anywhere else is it not an honorable thing to do.
Don't go around telling people you are a blue belt or "blue belt level" or anything else. That's just lame and shows insecurity in your own skills. It is like saying you have a college degree without actually going to college. Even if you are self-schooled, it isn't the same. Be completely honest instead - mention you grappled for 7+ years and won some blue belt competitions if it comes up - and then destroy them on the mat if you wish.
Frodo summed it up nicely I think. Although we obviously do feel similar about a lot of issues because we have trained together so much.
I don't have any real rank in the art of Judo. Despite that, I have actually trained Judo in legitimate pure Judo schools for about a year or so in my life. I have definitely learned something from that, so I think I do know something about Judo, even if it is admittedly just a little bit.
At one school in particular I trained at, we would have shiai (competition) at the end of class. Although it was not a regular tournament, it was shiai rather than randori. The idea was to win the match, and everyone fought their best as if it were a competition.
I was a blue belt in BJJ at the time, and I was able to defeat higher belts in Judo on a regular basis. So in that sense, I have done the same thing in Judo as you have done in BJJ.
Nonetheless, were I to walk into a Judo school today, I would put on a white belt. I would do so because nobody promoted me in Judo, and if I were to wear that rank in such a school, people would assume I had been. I would explain my background to the instructor of course since I would probably seem a little out of place.
Ultimately, it is your own personal choice what rank you choose to wear. No one can stop you from putting on whatever you feel is appropriate. However, I think it is wise to note that there are definitely some people out there (especially in BJJ) who will hold something like that against you.
I'm not saying it's right or wrong; I just want you to realize that a lot of places, it might be more of a big deal than you initially think.