The first Dr. Morbius appeared in the 1956 film "Forbidden Planet". Name in full: Dr. Edward Morbius, a man with a boosted IQ and a twisted ego to match. The name, Dr.Morbius, however, is a made-up name (which I will get to in a moment) which subtly, very subtly, refers to a twisted nature specific to a man with an over-abundance of genius.
A 1971 issue of the comic book, Spiderman, featured a character named Dr. Michael Morbius, PhD, who, while conducting chemical experiments, turned into a vampire. He was, initially, a nemesis of Spiderman (who, it seems, never seems to run out of nemeses). Marvel Comics later revived the character as a misunderstood superhero, as if Marvel didn't have enough of them.
In a 1976 episode of Dr. Who, called "The Brain of Morbius", a renegade time lord named Solon (a name borrowed from a 6th century BC Greek lawmaker who is credited with laying the foundations for Greek democracy), who probably appropriated the name for vain reasons, is seeking to revive the brain of Morbius, another renegade time lord who was done in by the time lords for his crimes. Solon had plans to revive Morbius by revitalizing his brain.
So, you ask, whence this name Morbius, always, it seems, representing a twisted character with great power?
Here is my speculation. Real nerds, like the creators of these characters, have at least a nodding acquaintance with advanced mathematics. Thus, they would have known about the inventor of a twisted band with a single side (not an inside and an outside, which would make two sides).The inventor of this object, or, if you will, its discoverer (which is how mathematicians usually think of such things) was a German mathematician named August Ferdinand Möbius. Today this one-sided object is called a Möbius band. (Actually, the band was discovered simultaneously - as mathematicians consider simultaneous discovery - by another German mathematician named Johann Benedict Listing. At least Wikipedia lists him as a co-inventor. They discovered the object in 1858.)
Since these sci-fi inventors knew their fans would have some difficulty with the name Möbius, the decided to change the "o-umlaut" to "or". The thing about a Möbius band is that it is twisted by nature, and, as a result, has only one side. The above characters all have in common that their personalities are twisted (and, if you will, even their minds are twisted) and they can only see one side of things, namely, their side.
By itself, the Möbius band is a beautiful mathematical object, and you might say the name and its use were twisted into a tabloid shape suitable to a mass sci-fi audience.
It seems appropriate to bring this up in a time in history when so many people can see only one side of an issue, even some people with PhDs and substantial brains.