What is the origin of British/Irish cinema names?
Solution 1:
Savoy
The Savoy cinema opened in 1920 in Bradford/UK.
The Savoy Theatre opened in 1881 in London on the site of the old Savoy Palace.
The Savoy Palace was built on the land granted to Peter II, the Count of Savoy in 1246.
I'd say that the cinema name was derived as follows:
Count of Savoy > Savoy Palace > Savoy Theatre > Savoy Cinema
References:
http://www.kingsdr.demon.co.uk/cinemas/savoy.htm
http://en.wikipedia.org/wiki/Savoy_Theatre
http://en.wikipedia.org/wiki/Savoy_Palace
http://en.wikipedia.org/wiki/Peter_II,_Count_of_Savoy
Curzon
Apparently, it's just a family name. Note that this was not the original name of the cinema. The original name was "Picture House".
In 1945 the cinema (previously known as "the Picture House") was sold and changed its name to the "Maxime".[2] Another change of ownership in 1953 brought its current name.
References:
http://en.wikipedia.org/wiki/Lord_Curzon (for the family name)
http://en.wikipedia.org/wiki/Curzon_cinema
Note: Odeon and Adelphi are already on FordBuchanan's interesting answer.
Solution 2:
Odeon is derived from the name for an ancient Greek building used much like a contemporary convert hall. It was used as a name for cinemas in Italy and France before the Odeon chain was set up in the UK in the 1930s.
The Adelphi Theatre in London was named after a terrace of houses that used to be opposite, Adelphi Buildings. The area took the name Adelphi, and the theatre from that. As with Odeon and Savoy, names of cinemas were often taken from existing names for theatres.
The Curzon in Mayfair, London, takes its name from the street where it is located. As it opened in the 30s, I'd imagine that other Curzons are named after it.