No, they intially wanted to name the airline "Swiss Airlines", and before the "new airline" started it's operations, some aircraft and some paper material were branded with this name (I guess even the first timetable).
For avoiding troubles with the obligees of Swissair because of the very similar name, the management decided to put the world "international" in between - a few days before the old Crossair became officially our new national carrier.
The short brand name is just SWISS, indeed.