By adding, "of Western NY", to me makes it sounds like it is a branch or in some way affilliate with "Stage Left Productions".

 

Find something unique in your area, something your area is known for and come up with a name based on that.  For instance a very quick google told me the area is referred to as the "Western Door", so how about "The Western Stage Door".  OK, maybe that's bad, but try that kind of brainstorming for a name.

 

If the name of your company includes your legal last name, you pretty much can do as you want--Otherwise you must file a DBA (doing business as) form.  This serves tax purposes and also makes sure that people can find out the owner of a company (if they get ripped off and need to sue).  If you are a corporation (even an S-corp) incorporation takes care of the DBA, because people can look up the legal owners to find them.

 

Example: "Smith's Production Company" or "Jones and Sons Plumbing" don't need a DBA, but "A+ Best Plumbing" would need a DBA. 

 

I started two companies.  The first needed a DBA, (sole proprietorship with a name that didn't include my legal last name) the second I incorporated.  Incorporation took care of DBA.

 

Now to your question... But this second company has a name that is used in other states for other companies.  This company has been around 19 years.  Some of those other companies had started before I did, others started later.  To my best knowledge this is a problem if the state of Michigan has two "ABC Productions, Inc."  And yet not a problem if California and Michigan each have an "ABC Productions, Inc."

 

Of course you can always contact legal sources for real advice.  But the safest course is to use your last name.  The second safest course is to make sure your state doesn't have a similarly named production company.  Then think hard whether the confusion of similar companies with similar names will be an issue.  Choose a name that makes it clear what business you are in.  Choose a name that has marketing potential.  Example if you were in the city of 'Bartholomew', you might name your company "Bartholomew Productions" leading to easy campaign slogans like "For the Best Productions in Bartholomew, choose Bartholomew Productions!"  Smart if you are limiting yourself to the city of Bartholomew--but then stupid if you grow way past that city.  Like I said--think hard and test market the names.

 

Personally I sorta warmed to " My Other Stage Left Productions" and "Dragon Flight Productions"

 

Best of luck.