Do you define it by purpose? By historical coinage of terms, chapel, cathedral, etc, etc? By denomination, like house of worship, house of prayer type names? By region, just think Northeast versus mid-South? Secular type names to appeal to anyone, such as auditorium?
Something that sounds so simple actually can have impact various ways.
A simple search yields some intriguing but not helpful ideas for your typical evangelical church:
For instance, some synonyms aren't the best:
And there's the connotation that the sanctuary is somehow more holy than other parts of a church or one's life outside of it, which is a dubious claim. The only thing that makes that so is that the Word of God is sung and preached in a sanctuary verbally and in hearts. But if you consider the place, what does it mean to call it sanctified, aka sanctuary, what does that end up saying? Does it convey what we want in a more evangelical world of churches? We do not buy into any kind of innate holiness to it, and it is not the old Temple of Israel. It's interesting.
Here are more ideas related to it connotation in today's culture, which give us pause mostly, though not everything in the definition:
Then there's a lot of clutter from outmoded religious terms from the past that people will not get today, such as at this architecture site: http://www.kencollins.com/glossary/architecture.htm
Other names are simply off limits, because they imply cult stuff, like the name "hall" is a no go, since a very active false religious group uses that for their buildings in every decent village town and city of size.
Assemble is good, and very biblical as far as theology of the New Testament, and yet it would to the person on the street imply like a high school or football or work assembly, unfortunately. It would take work to fill it with new meanings.
Maybe worship center is still the reigning champ then of names for where we assemble.
Thoughts welcome, God bless!