There are two Demeza threads in the UK the others tend to use DeMeza and have Rachelina de Haas in the tree but came to the Midlands a lot later than Isaac a stock brocker of Spitalfields. Both threads came to UK from Holland as Jewish Shephardi. There is a casa De Mesa in Toledo old town in Spain, a De Mesa was rewarded into nobility for fighting the Moors at the time of El Cid.
I have read of a DeMeza in America with the Conquistadors. The earliest in north America were in the 1600's in San Francisco (Spanish territory at that time) There are hundreds of DeMeza's in Mexico but all of a different thread.