I only hobby when I travel, to lower the odds of getting outed.  I have recently moved beyond strictly closed-door sessions with one provider.  We had our first dinner date recently. So there is a small chance that I can be discovered. She brought up the question of a cover, as protection for me.  I don't have one, and am attempting to be creative.  

your home or business.

traffic areas.  Lies are dangerous...  probably a coworker or client is the best cover but it's hard to explain away a romantic dinner.

I'm in the Fashion/Apparel industry and I'm always have lunches and meeting with Designers and owners of model agencies. So if anyone should see me with someone, I'll just say she's a client...Funny, in LA I was once actually having lunch with a agent from Korea. she was very attractive looking. So my wife's friend husband came by to say "Hi" when we were having lunch. I made the intro and I thought all was done, no issues. Well when I got home that night, my wife asked, "so who did you have lunch with?" Dude told his wife.....Now that guy, is blackballed by the guys in our "inner circle"..His man card has been revoked.

And it makes it even better if each of you are Dressed casually, Business Casual, ie: appropriately for a lunch or dinner, etc...  (In other words-be sure she isn't wearing hooker shoes, etc....)

Simple first name introduction, then I'd say "good to see you, but we are involved in conversation, maybe we can catch up later".

I've been at dinner with a business colleague and/or Customer and had someone approach, a simple first name introduction is suffice, they aren't going to be around long enough for a last name to matter as I'm not there to see the person who interrupted.

Divorce

You didn't tell us what type of work you were involved in, but you can perhaps go with a story that you are investing in her opening a small business. To keep the details private or very vague, no one would raise an eyebrow as that is generally the case with new businesses anyways. And its not too far from the truth  

I don't have a SO, but I have some nosey colleagues, friends, and relatives that would ask all sorts of questions if they saw me with a lady who was young enough to be my daughter.  On one occasion, I did bump into a good friend when I was out on a dinner date, but I just introduced her as a friend who was visiting from out of town and left it at that.

Went to see that movie in a theater twice !! I laughed so hard it is a wonder they didn't ask me to leave !!

Or perhaps she's an estate attorney, or a financial planner.  Maybe she's your therapist and dinner is an exercise in which she's intentionally stressing your social anxiety with the goal to build up your tolerance levels.

His first sentence says he only hobbies when he travels, so I think he got that covered.

Sexual Surrogate if it is a friend, then go back to the Divorce Attorney
Then enjoy the meal, drinks and after meal entertainment.
Full disclosure, I've been divorced three times.
Best Regards!

First name only introductions are very common.

You're being scouted by another firm and agreed to meet out of town to minimize the chance of coworkers discovering it.  Haven't told the wife yet since you wanted to see what the offer was.  If anyone tells the wife then you can say it wasn't an appealing offer and had declined.

A while ago, a provider friend who is an observing Christian said she would love to go to one of of the wonderful Sunday organ recitals at the National Cathedral in Washington DC, and asked me to take her some time.  My SO was out of town so I picked her up and escorted her to the concert.  Of course she was dressed conservatively and attractively, not distinguishable from any of the other parishioners.  She honestly enjoyed the music, and afterwards I took her to a local restaurant.  All of this OTC, by prior arrangement.  Nevertheless, a neighbor saw us in the Cathedral and reported to my SO.  When confronted, I told the truth -- a provider I had gotten to know as a friend asked me to show her the Cathedral as part of her religious interests, and I complied.  
Well...I occasionally hear about this from my SO, but the fact that I gave a mostly factual explanation while eliminating some details helped salvage the situation, with some residual damage to mutual trust with my SO.  She has forgiven, maybe, but not forgotten.  But it is ironic that my act of facilitating an honest Christian believer who happens to be a wonderful provider to something that was religiously and culturally important to her got me in trouble with my SO.  What bothered my SO of course, was not that I "took a sinner to church" but that there was an underlying connection that shouted in loud words "INFIDELITY!!!"  Life is difficult.

...she better perform a recital on my organ afterwards too!!

...It all depends on your attitude and how you carry yourself.  The Peter Pan Syndrome works great for me - no responsibilities, life's one big party.  I could be with someone 30 years younger than me and she'd still be more mature.

I've really used this one.

you had been to a strip club together.  People are funny that way.