Is there a specific term or name for Tim Burton's Gothic dark comedic style?

It doesn't answer your question directly and with a single term but I guess it couldn't/shouldn't be answered as such, too. "German Expressionism", "Gothic Suburbia" seem to be likely terms to distinguish his style.

From the article written by Martyn Conterio:

His visual style is unique, bringing together 19th and 20th century European art aesthetics and American kitsch. Stories very often focused on freaks and loners that should, in theory, make studio executives run a mile. But they don’t. Burton’s brand of quirkiness connects with millions and his films have universal appeal.

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COSTUMES
Anybody that has seen a Tim Burton film will recognise that the director has a fondness for costumes with a 19th century Victorian flavour, even if the story is set in more modern times. But he is equally inspired by the famed stories and cartoon drawings of Dr. Seuss. This can be seen time and time again with characters wearing an array of clothing designed in black-and-white stripes. Elsewhere, leading ladies and heroines often sport flowing blonde locks, pale white faces and exquisite gowns akin to Pre-Raphaelite paintings. Burton is a man steeped in the history of art and his synthesising of different periods and eras is humorous and striking.

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GERMAN EXPRESSIONISM
The director described the famous German art movement in the book “Burton on Burton” (Mark Salisbury, 1995) as like “the inside of somebody’s head, like an internalized state externalized.” It’s not just chiaroscuro lighting effects, but also in the production design and the wildly exaggerated sets and décor. Just think of the Inventor’s castle in “Edward Scissorhands” or the whole of Gotham City in “Batman Returns.” Burton’s cinematic universe is indebted to German Expressionism.

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GOTHIC MEETS SUBURBIA
The director’s visual imagination often sees Gothic architecture and atmosphere brought together with his own upbringing in sunny Los Angeles. It shouldn’t work at all—a world of darkness, wild moors and haunted castles crossed with pastel-coloured bungalows, picket fences and verdant green lawns as American as apple pie. And yet in merging these unlikely worlds, Burton struck creative gold. The contrast is there in nearly all his films. The ruined castle perched above suburbia in “Edward Scissorhands” is a classic Burton touch. Gothic suburbia is revisited again, in animated form, in “Frankenweenie.” In “Dark Shadows,” the Gothic mansion owned by the Collins family is hidden back in the trees above the fishing port of Collinsport.