It seems to me that there are 2 main objections to you wearing 10th Planet paraphernalia:
1) It is disrespectful towards the gym where you normally train.
2) It is disrespectful towards 10th Planet; you haven't "earned" the right to wear our name since you haven't trained with us.
I find both of these claims to be very weak; I recommend wearing whatever is comfortable and gives you any sort (even trivial) competitive edge (e.g., better grip, intimidate opponents). In the following, I'll examine each claim separately.
Claim 1: It is disrespectful towards the gym where you normally train.
I reject this claim for two reasons: a) you are paying your gym, and b) winning your matches precedes marketing for your gym.
Presumably you are paying both your gym for training and the tournament organizer for the chance at competition. Because you are paying for both of these things, you have the right to represent any organization or philosophy you choose. If you feel that you've learned much from MG in Action, or Gracie University, wear those rashguards. If you simply feel that MG or Gracie are more intimidating names that will mislead your opponent into making mistakes, wear those names. If the rashguard you bought at Walmart for $8 is supremely comfortable, fits your thick-ass neck better than anything else, and breathes well so that you cool more efficiently, wear that (<- this was an autobiographical sentence). If you want to wear a PETA rashguard so that you can channel the power of awe-inspiring sea mammals, wear that (<- this was not an autobiographical sentence). If you feel like the Palestinian diaspora is woefully underrepresented in the popular consciousness, wear a Hamas rashguard. If all of your spiritual strength comes from the love of Christ, wear a shirt with a big-ass cross on it.
It is your life, your money, your body, and your competition.
Claim 2: You haven't "earned" the right to represent 10th Planet
I reject this because I believe we have a pretty low threshold for "earning" the right.
Our (Eddie's) philosophy has always been one of abject open-mindedness. We "steal" techniques from anyone if they seem to be useful (or if they look cool), and we teach everyone we can (for a minimal fee. I mean seriously minimal. Go try to find a Gracie Barra price list. I'll wait.). We want this system and this mentality to spread across the land like the black plague, improving jiujitsu, making it more exciting to spectators and more welcoming to beginners, and generally increasing the sum total of badass in the world. We design super sweet rashguards so that people buy them and wear them and look amazing while competing and training.
To me, if you love jiujitsu, are humble, want to learn all of the effective techniques that you can, and want to help spread this great sport as much as possible, you are 10th Planet. Watch Mastering the System, read Advanced Rubber Guard, buy that rashie, and wear it. You've earned it, Playa, as much as I have.