Is ultimate Frisbee a Proper noun?

No, "ultimate Frisbee" is not a proper noun. The term "ultimate" refers to the sport itself, while "Frisbee" is a trademarked name for a specific brand of flying disc. When referring to the sport generically, it is often written as "ultimate" or "ultimate disc." However, when "Frisbee" is used in a brand-specific context, it functions as a proper noun.