While there have been some attempts to attach theological significance to gargoyles, the name seems to derive from their drain-spout function. The artists probably thought it was a lot more fitting to have streams of water coming at you from something that looked nasty than to have it coming forth from a saint.
And we should be thankful that the drainage system has at least been partially salvaged.
Bernard of Clairvaux spoke out against such gargoyles, which certainly also applies to later grotesque versions:
What are these fantastic monsters doing in the cloisters before the eyes of the brothers as they read? What is the meaning of these unclean monkeys, these strange savage lions, and monsters? To what purpose are here placed these creatures, half beast, half man, or these spotted tigers? I see several bodies with one head and several heads with one body. Here is a quadruped with a serpent's head, there a fish with a quadruped's head, then again an animal half horse, half goat... Surely if we do not blush for such absurdities, we should at least regret what we have spent on them. ("Apologia ad Guillelmum abbatem.")
Gargoyles and other mythical creatures also represented and illustrated evil in the medieval Catholic Church.
Several are not even true gargoyles at all. In fact, the creatures that adorn Notre Dame cathedral are made up of various types of fantastical beasts, including: chimera, which are ornamental only and serve no real function; grotesques, which are carvings that may or may not carry water; a wyvern, which is a small 2-footed dragon; and the Styrga
While the true gargoyles were prone to erosion from the very rainwater they were designed to carry away from the cathedral, many other figures were removed or destroyed in the 17th and 18th centuries, particularly during the French Revolution.
They were later replaced in the Gothic style by the French architect Eugène Emmanuel Viollet-le-Duc during his 25-year restoration of Notre Dame in the mid-1800s. As was not uncommon among earlier medieval church builders, Viollet-le-Duc added a figure of himself as one of the new gargoyles. - https://www.thevintagenews.com/2018/11/24/gargoyles-of-notre-dame/