jiu jitsu is perfect. it is what it is. brazilian jiu jitsu sounds even better. i personally think it sounds much better than "wrestling", "grappling" or "submission wrestling", etc.
I'm with you. Me and some friends hired out a hall in the local leisure centre with some matts recently (they train elsewhere and we sometimes like to roll). In the next hall was the local karate/kungfu martial arts organisation having their grading. In the hall were people with multicoloured belts, every colour of the rainbow, 9 year old kids with blackbelts, and all calling their instructor "Master".
When they asked what we do, felt good to say Brazilian Jiu Jitsu. Not to sound gay but am proud to say I do it. Just remain humble and don't rise to those who relate it to stupid arts, it's not their fault - some people just aren't into that sort of martial art/sport and therefore know nothing about it.
One thing I love though is when my fiance's ma asks her:
"When are they going tumbling next?"