"Gucci" does not have a full form; it is simply the brand name itself, derived from the founder, Guccio Gucci.
The name "Gucci" represents the legacy of its founder and the brand's Italian heritage. It’s not an acronym or abbreviation. The luxury fashion house was established in Florence, Italy, in 1921 by Guccio Gucci. The name has since become synonymous with high-end fashion, leather goods, and accessories worldwide.
Therefore, attempting to expand "Gucci" into a longer phrase would be inaccurate, as the name functions solely as the brand's identifier.