As a general rule, copyright does not protect single words or short phrases, even if those words or short phrases are nonsense.
Tell it to the Hand. There is an odd collection of copyright cases that indicate that nonsense words may be protectable in different contexts. In a case in which a book of meaningless code words was protected (Reiss v. National Quotation Bureau), the great jurist Learned Hand (and odd-couple pal to J.D. Salinger) wrote, "Conceivably there may arise a poet who strings together words without rational sequence-perhaps even coined syllables-through whose beauty, cadence, meter and rhyme he may seek to make poetry." (Hand's logic in that case was later used as the basis for protecting Apple's operating system object code. The protection of inventive words was part of the copyright-software debate in the late 1980s since nonsense words (source code) are essentially what facilitate our 'human-machine' communications.)
The Jabberwock. In another case, the great Justice Jerome Frank also mentioned a phrase from Lewis Carroll's Jabberwocky, "Twas brillig and the slithy toves" as an example of a nonsense phrase with sufficient originality to achieve copyright protection. There's also a case involving the word 'Supercalafragalisticexpialidocious' in which the court held that copying an inventive word could 'conceivably' create liability. And finally, a British court reviewing the word "Exxon' indicated that inventive words might be protected in some contexts. So, it's possible a sufficiently original collection of coined words will be protected.
When inventive words are character names. If you use the inventive word as a character name, you can likely achieve trademark protection without much problem. You may also get some peripeheral copyright protection for the character name as well -- for example, in one case, merchandisers were stopped from using the phrase "E.T. Phone Home" under copyright law.