A quick google shows Strand theaters in California, Massachusetts, Manhattan, Maine, Michigan, Plattsburgh, Louisiana, New Jersey, and more. Many of them are old - early 20th century or so, from what I can see online and from my experience going to some of them.
Were they all originally franchisees or part of a chain or something? Or is calling a theater 'Strand' simply tradition - and if so why?
'The Strand' is a street in central London that once housed several famous theatres, including The Globe (though this was merely named after the original known for housing Shakespeare's plays). Essentially it was a Victorian era Broadway. Most of the theatres have since shut down (but not all of them) which is why this would have been a better known name a century ago when your American theatres were being named.
An unrelated fun fact: the original Twinings tea company is also on The Strand.
As a follow up- one of the main roads in London's West End (home of many theatres) is called 'The Strand'. Is this related?
To add on what /u/dvb70 said,
Well The Strand in London got it's name due to it running along side of the Thames so its name is linked to that meaning.
Strand is a word that comes from Old Norse and which means beach.
Let me piggyback: what about "Savoy" and "Majestic"? Aren't these also common?