Neo, from the Greek neos, is a prefix used in English to mean new, for example in neologism (lit. "new word").
It is frequently used by fledgling authors (more likely fanboys over fangirls in this case) as a name to give to a character with whom they want to invoke a sense of mystery or power, or used as a part of some really cool concept or device. It is a generic 'cool' name or word, and can be found in bad science fiction gibberish as often as it can be found as a name or name part.
The trend for even considering this language part as a name likely derives from the most known example: the lead character Neo from The Matrix.
Other uses may include the names of movements and resurgences in historical context--Neoclassicism, for example--and authors often use it to construct concepts in-universe. It would not be unheard of for a science-fantasy character to practice 'Neoshamanism' or something.
How silly depends on the universe and the usage.
Other 'cool' greek prefixes include xenos, umbra, aqua, archos, dominus, geo, ideos, liber, mania, mortis, and solus.