What is a name for a play place?

Depends on the subject matter of the play. Titles are tricky, they have to draw and audience in and give a hint as to what's going on in the play. Audiences can easily be interested or turned away by a title.

So, to choose a title, first look at the subject matter and the tone - if it's a comedy you don't want a title that evokes drama.

What images come to mind with the play, that's a great place to go with a title. Images create pictures in the minds of the audience. What's the main image in the play?