Some of them ask for it in their screening. They use it to look at your reviews, and in some cases your board posts. It gives them a better feel for who you are as a person.

if she asks, give it to her-why wouldn't ya what have you got to hide?

I've seen realitively few new ladies since joining TER...  but I have on occasion offered my user name...  or set up a meeting...  through TER.  There is nothing in my reviews that I'm ashamed of...  
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Personally, I'm in the camp that provides my screen name with the appointment  request.  I believe that it does help the lady to go through my reviews and posts (if she cares to take the time), but it HAS bit me in the ass.  

Some (few) ladies will use that information to muzzle what you can say about your encounter in a review or the forum.

Want to talk about the lady who called my HOUSE several days after she NCNS'd me?  She just wanted to make sure I knew she could fuck up my life if I said anything publicly.  No, I never did and never will...

My SN is me.  If you have something to hide, then why even be here, your SN is an alias anyway.  You want to see a lady, be as honest as you can afford to be, you will get the best results that way.

Swim