The problem is that "Ultimate" also is the everyday name for "Ultimate Running".
Both of these options are better than deciding that we should integrate the branding that the ultimate folks are now trying to hard to avoid. (Referencing it as "Ultimate Frisbee" would be rather narrow sited as "Frisbee" is a rather specific brand name. Most flying discs are now made by several other companies at this point (Discraft, Innova, Wham-O (makers of the iconic "Frisbee)). While the branding is part of the common parlance there is little reason anymore with other manufacturers making very good flying discs. (This is very similar to how Disc Golf has fought against the "Frisbee Golf" name).