From what I understand King owns the word "saga" as it pertains to video games from this article - http://www.polygon.com/2014/4/17/5624980/king-settles-trademark-disputes-with-the-banner-saga-developer
But I can't tell from the article or from copyright record searches whether this is actually true, and since the developers of "The Banner Saga" settled out of court with King it doesn't help to explain either.
Would it be against copyright law to use the word saga in a name of a video game?
First of all, it's got nothing to do with copyright law. You can't copyright a word, or even a short phrase, whether or not it's a title. This is a matter of trademark law.
Second, it would probably not be a violation of trademark law, assuming the title is relevant to the work and you aren't trying to mislead people into thinking it's a King game. See the case Rogers v. Grimaldi (2d Cir. 1989), in which Ginger Rogers and the estate of Fred Estare sued over a movie which was titled "Ginger and Fred". Under the Rogers test, the title of an expressive work does not violate trademark law "unless the title has no artistic relevance to the underlying work whatsoever, or, if it has some artistic relevance, unless the title explicitly misleads as to the source or the content of the work."
However, it is very possible that you'd be sued by King, and it's even possible you'd lose. While the Rogers test has been adopted by other circuits besides the 2nd (for example, see the case Fox v. Empire, 9th Cir. 2017, in which the Rogers test was applied and the court found that the title of the TV show Empire did not violate the trademark of Empire Distribution), it probably hasn't been adopted by every circuit, and I don't think the Supreme Court has ruled on it. And King has shown they're willing to take people to court over this.
