The original Vstrom was 1000cc.
Then they made a 650.
To differentiate, the big one was called a vee, and the smaller one a wee.
Then they changed the 650 motor to the Gladius 650 motor. A Gladius-engined wee became a glee. GL for gladius replacing the w.
Then they put beaks on.
A vee with a beak became a Veek.
A glee with a beak became a gleek.
These are just casual nicknames, its easier to say "I traded my glee for a KTM" than "I traded my Suzuki dL650L2 for a Kraftfahrzeuge Trunkenpolz Mattighofen."