Copyrights and Trademarks are two separate things, even though in comics they usually apply to one character. Owning a copyright to a story has no affect on the status of a trademark, just like owning a registered trademark for a character/name does impact the copyright of a story.
Marvel has copyrights for Spider-Man's stories, keeping the character from becoming public domain. Marvel also has to separately file for Trademarks on the name, logo and select images (used for merchandising) to keep anyone else from creating a comic, movie or coffee mug using the name "Spider-Man". Trademarks, unlike copyrights, have to be constantly used. Last time I checked, Marvel (for example) has to file paperwork practically every five years to let everyone know that they are still actively using "Spider-Man" as a registered trademark (and pay a fee every ten years). Otherwise, the name is considered abandoned and anyone else can swoop in and take the name. It's this very reason why Marvel keeps producing books entitled "Captain Marvel", "Ghost Rider", "Doctor Strange" and many others every few years.
Sometimes, creators strike deals with publishers to produce a comic/story while the creator retains "ownership" of a character. George Brenner's "The Clock" is an early example of this, as wherever he went, The Clock followed. For lack of a better term, think of these cases as "licensing deals". Even though the stories published may be copyrighted by companies like Quality or Charlton, the creator still owns the character, and when he ends his association with one company, he effectively ends the deal and can take the character with him to another. The mistake that Morisi, Brenner and Eisner made was that the copyrights to those stories were not filed under their name but by the publisher, with the result being that the stories entered the public domain once the copyrights expired (which was immediately upon publication in the case of many of Charlton's books).
Again, the status of the copyrights have no affect on any trademarks, so Morisi's estate can own the trademark on "Peter Cannon: Thunderbolt", DC can own the name "Blue Beetle", Marvel can have "Captain Marvel", while Eisner's family can own the trademark for "The Spirit". The names are off-limits for things like a comic book title even if the original stories/character designs are, in reality, public domain.