As it was said that she is Scandinavian, it is likely she was born in Denmark, Norway or Sweden (either way, she's in Europe). Her name is likely short for Alexandra, which Claire didn't know. Her trip was sponsored by Miss Shannon through her school, and Claire's parents agreed to host Alex. This was arguably due to the name confusion, Claire thought Alex was male and likely some hunky European, and expressed disgust when Alex was seen in person. Claire's anger turned to jealousy when her classmates got along well with Alex, likely because she was not stuck up like Claire. Claire proceeded to ruin Alex's reputation, which caused Beetlejuice to seek revenge. Beetlejuice, through help from Lydia, create a Potemkin village in the Neitherworld called "Scrunglevania", then fool Miss Shannon into saying Claire has been approved for a foreign exchange program.