It is not that “Gaudy” comes from the Catalan surname “Gaudí” but both words come from the same Latin word “Gaudēre” that means “to joy” or “to enjoy”, "to rejoice” or “be merry”…
“Gaudy” most likely comes from the ancient English word “gaud” that comes from the French “Gaudir” which, like the Latin word where it comes from, (“Gaudēre”), means “to joy” or “to enjoy”, "to rejoice” or “be merry”
We can also find the word “Gaudir” in the Catalan language having the same mentioned meaning and the same Latin origin as its French equivalent.
Derived from the Catalan verb “Gaudir” we find the Middle Age noun word “Gaudí”. A “Gaudí” was anyone who, even thou he was not a cavalier, militiaman, honourable citizen, or titled noble, could enjoy [“gaudir”] (that means; to have) the privileges of the military class due to his job or status [See “gaudí” entry in the official Catalan language dictionary at http://www.diccionari.cat/lexicx.jsp?GECART=0069107 ].
In the Middle Age people started to be differentiated one from the others by their job (like “Smith” or “Herrero” in Spanish), origin (like “Oxford” or “Toledo”), condition (like “Bald” or “Calvo” in Spanish ), or status (like “Cavalier” or the one that occupies us; “Gaudí”), etc. That was the origins of the surnames and the origin of our famous catalan architect Antoni Gaudí’s surname.
So here you have been explained how there’s really a connetction between “Gaudy” and “Gaudí” but an indirect way.