When a work uses a character from a previous work by a different author, it may become a derivative work. Derivative works include translations from one language to another; transformations in form, such as from prose to film; unauthorized sequels; and other cases where one work is "based on" an earlier work. Protection for the creation of derivative works is a relatively late addition to copyright law. US law did not start to protect this until the 1870s, and it was not fully implemented until the copyright act of 1909.
Significant use of a distinctive character is one way of basing a work on a previous work. But the character must be distinctive, not generic. In *NICHOLS v. UNIVERSAL PICTURES CORPORATION et al. 45 F.2d 119 (1930) the court write, in an often quoted passage;
Nor need we hold that the same may not be true as to the characters, quite independently of the "plot" proper, though, as far as we know, such a case has never arisen. If Twelfth Night were copyrighted, it is quite possible that a second comer might so closely imitate Sir Toby Belch or Malvolio as to infringe, but it would not be enough that for one of his characters he cast a riotous knight who kept wassail to the discomfort of the household, or a vain and foppish steward who became amorous of his mistress. ... It follows that the less developed the characters, the less they can be copyrighted; that is the penalty an author must bear for marking them too indistinctly.
In DC Comics v. Towle, No. 13-55484 (9th Cir., September 23, 2015) the court held that the Batmobile was a protected element, and making models without a license was an infringement. In that case the court wrote:
[n]ot every comic book, television, or motion picture character is entitled to copyright protection. We have held that copyright protection is available only “for characters that are especially distinctive.” . . . To meet this standard, a character must be “sufficiently delineated” and display “consistent, widely identifiable traits.” . . . Further, characters that have been “lightly sketched” and lack descriptions may not merit copyright protection.
Third, the Batmobile is “especially distinctive” and contains unique elements of expression. In addition to its status as Batman’s loyal bat-themed sidekick complete with the character traits and physical characteristics described above, the Batmobile also has its unique and highly recognizable name. It is not merely a stock character.
Note the stress laid on the distinctiveness of the name. A name as such, like a title or a short phrase, is not subject to copyright protection. it is not a "work of authorship". But a name can be one aspect of what makes a character distinctive, and excessive use of a distinctive character from an earlier work can make the later work a derivative work in the legal sense, even if not in the literary sense.
This article on "Infringing Cartoon Characters" says:
The standard for copyright infringement is “substantially similar” artistic expression. “Substantial similarity” is measured by whether a normal observer would recognize the second work as a copy of (or derived from) the original. For cartoon characters, courts consider not only the visual resemblance but also narrative aspects of a character, such as their personalities, behaviors, biographies, and story lines.
In Warner Bros. Pictures, Inc., v. Columbia Broadcasting System 216 F.2d 945, 104 U.S.P.Q. 103 (9th Cir. 1954), the character Sam Spade, from The Maltese Falcon and other works, was held not to be distinctive enough that new works about the character would be infringements. This case was complicated by conflicting grants from the original author. This case might well be decided differently today.
In Dr. Seuss Enterprises, L.P. v. Penguin Books 109 F.3d 1394 (9th Cir. 1997), the defendants, in a book called The Cat NOT in the Hat, told the story of the O.J. Simpson murder trial in the style of the Dr. Seuss children’s classic The Cat in the Hat. The defendants took the main character from the copyrighted work and reused it in order to tell a new story in a similar style. This was held to be an infringing derivative work.
In this legal analysis article, the author, Ivan Hoffman writes:
Further still, even characters that remain under copyright protection can be used in other works to the extent that such other use falls within the scope of the fair use provisions of United States copyright law. One recent example of this situation is in the “Wind Done Gone” case, in which the protected characters from “Gone With The Wind” were parodied and in which the Court upheld the right of the subsequent user to do so under the said fair use laws. But such a defense was not successful in a case involving the characters from the Seinfeld television series.