The title of the movie reflects how the name is pronounced and how Beetlejuice himself tricks Winona Ryder’s character into speaking his name and consequently making him appear to cause trouble; he can’t say it himself, so he plays charades and makes Lydia see an anthropomorphic beetle and a carton of Minute Maid, in that order. However, in the movie itself beyond the opening credits, the name is spelled Betelgeuse. The name shares it spelling with that of the brightest star in the constellation Orion. According to Wikipedia, this celestial body gets it name from the Arabic al-Jauzā, a feminine name. But beyond that, the origin is uncertain. Some sources state that the name can be roughly translated as “the central one.” It may have been a transcription error with the name Yad al-Jauzā, “the hand of al-Jauzā,” that led to the name Betelgeuse. If that first letter — represented in the Arabic alphabet letter “ﻴ” — was misread as a “B,” then it could have given rise to what we non-Arabic-speakers call the star today. During the Renaissance, the star’s name was written as Bait al-Jauzā, “house of Orion,” though it was apparently believed that this meant “armpit of Orion” widely enough that the current Persian name for it is derived from this. Still others think it was always Ibṭ al-Jauzah, “armpit of Orion,” at least until it degenerated into forms such as Bed Elgueze, Beit Algueze, and Bet El-gueze, which would have led to the non-Arabic name for the star.
It’s worth noting that the very reliable Online Etymology Dictionary just offers “armpit of the central one” without any notation of the apparent controversy about where the term actually came from.
I haven’t found any associations with the star that seem like they could have inspired Tim Burton to name his most famous demonic character in its honor, but Wikipedia does point out that shellac can and probably does contain crushed insects and is therefore sometimes referred to as beetlejuice, though this fact is appended with one of those superscript “citation needed” notes, so who knows if this is actually enough of a thing to have influenced Burton. But hey — at least take this as news that food products that use shellac, such as Skittles, are not vegetarian-friendly.
