I can barely remember people's names in real life. So, all the more, when someone takes the right measures to be remembered, it makes a HUGE impact.
I think all guys in SC's (many would never admit it) are looking for a human CONNECTION--even if it's imaginary. But a "pretend human connection" is still...technically...a type of connection.
So I think the NAME CAN BE very important to the patron on an emotional level and the Lady on a business level (*I highly respect the business/sales aspect of being a stripper).
That said, "traditional stripper names" like Diamond, Sparkles, Delilah, Star etc. are pointless. Not a problem, but it immediately shuts down the possibility of a top-rate connection.
An interesting "strategy" I feel I've encountered is the "my stage name is...Rose, but you can call me Rachel." When a girl does this, I still don't believe "Rachel" is her real name. And I don't care about knowing her real anyways (unless the friendship has grown and grown over dozens of encounters). Nonetheless, it's not much different than offering someone your "nick-name."
The ".... But you can call me ______, everyone does!" This is a very good approach.
An overly common name like Ashley may be better than Diamond, but easily forgotten (Though, again, "My name is Ashley, but you can call me Ash" half way through the encounter would make a difference.)
Another best approach would be a truly unique name like ... "Orchid" ... that is uncommon can stand out IF it comes with an explanation. Explaining one's name is always a great connection.
Lastly, sociologically, if a name isn't used regularly it loses its power. So "what's in a name" if it's only said once at the beginning and forgotten 15 seconds later.
Conclusion: use a name to connect, not as a mere title.
*I prefer only top notch professional beauties and establishments.