According to Gidget's computer when she identifies that Renton and Eureka have stolen the Nirvash, the computer says that Eureka's last name is "Zita." However, her birthplace, birthdate and therefore age are all labeled unknown.
The movie takes place in America some time between the 2040s and 2060s. So technology is only different regarding the Azo (which are the equivalent of Scub Coral).
Holland and his crew saw into the main anime timeline and saw the moon with Renton and Eureka's names. However, because they are American, they don't know it was Japanese.