I know a lot of people will disagree with me, but I think it's silly and possibly counterproductive, or worse, to lie about anything like this. So many escorts lie about their age, country of origin, cosmetic surgery, dress size etc. etc., and it makes us all look duplicitous or even scammers.
Conversely, I think we are 100% entitled to keep anything to do with our private lives private, so anyone asking my real name would get short shrift.
In this case, I don't think it would be wrong to not mention the BBLs on your profile, but if a client asked I would be honest and say yes - making a flirty joke about it possibly. No need to lie or be sensitive about it IMO.