According to the manual:
User variables... cannot be used directly in an SQL statement as an identifier or as part of an identifier, such as in contexts where a table or database name is expected
Which explains why what I've been trying doesn't work:
set @databaseName := 'job_hunt_2';
drop database @databaseName;
create database @databaseName;
use @databaseName;
Is there a way to accomplish this, or is it simply impossible? Thanks!