When can you tell people you are dating?

I don't have much time, so I'll keep this very brief.  When you are in the process of divorcing (or separating, in my case), when is it OK to let people know you are also dating?

I'm thinking of Debbie and me.  And I'm thinking that I haven't moved out of the house yet (or Wife hasn't ... the delay is exactly because we haven't figured out yet who's moving).  And my lawyer is working on the papers for separation but hasn't filed them yet.  On the other hand, Wife and I have had no real marriage for ... well, a long time, as you know.  And God knows Wife hasn't been terribly subtle about seeing her own friends.

It's an issue because Debbie and I live in the same town.  There's more of a risk that we might be seen doing things together than there ever was with D.  But also I'm farther along with the whole divorce thing.  My family knows.  The boys know. 

Are there reasons I still need to keep Debbie a secret?  Advice is welcome ....