Arizona
And before I am corrected, yes, I know that you cannot copyright a name.
I have a fictional character that is part of a group. On items featuring the character, I have "Character, Group, and all related characters are © me"
An individual with a group that has the same name is claiming that by doing this I am putting a copyright claim on the name. By phrasing it like this, am I claiming the names and not just the characters behind the names who otherwise fulfill the standards of fixation, expression, and originality? If it is the legal case that I am claiming the names as well, what can I do to make it clear I am not copyrighting the names of the characters, but the characters themselves?
Are these characters you have created part of a literary work or literary works?
You know already you cannot copyright a name. The name could become a trademark, however, when the character is used in a book series (like Captain Underpants) and/or gains a secondary meaning in the marketplace by identifying particular literary characters, works, or products developed from the literary works (like Mickey Mouse, Harry Potter, Snoopy).
The images of the characters that you have created are automatically copyrighted once you have fixed these characters in a tangible form, if they are original and creative enough (distinct from all other characters). There is no need for you to do anything more from a copyright perspective, although registering your characters with the US Copyright Office prior to publication of your characters makes you eligible for statutory damages should someone infringe (copy) your characters for use as their own.
You can identify your characters any way you want to identify them as long as they do not infringe on another's rights, be they copyrights or trademark rights. Therefore, if your characters are aliens, you can identify your characters as "Aliens" but if you identify your characters as "The E.T. Group," you would be infringing on the E.T. trademark.
If your characters are part of a literary work, they must be able to stand on their own to be offered copyright protection. Not all literary characters will be developed well enough to prevent others from using the same or similar characters in their own works. Using the E.T. example again: E.T. is protectable (both under copyright laws and under trademark laws) because the alien character is distinctive and has been developed and marketed as a unique alien character whereas an ordinary alien character on its own would not be protectable unless it has the creativity and originality necessary for copyright protection (although a literary work about this alien could have copyright protection).
Following is a link to a defining case (Nichols v. Universal Pictures Corp, 45 F.2d 119, 2d Cir. 1930) where Judge Learned Hand stated 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."
Nichols is followed by three additional cases you can review to see how courts look at fictional characters when determining if others can be prevented from using the same or similar characters and/or their names.
Nichols v. Universal Pictures:
https://cyber.harvard.edu/people/tfisher/IP/1930 Nichols.pdf
D.C. Comics, Inc. v. Unlimited Monkey Business, Inc, 598 F.Supp 110, Dist. Ct, ND Georgia, 1984:
http://scholar.google.com/scholar_case?case=2473265100776679658&q=trademark+copyrights+in+fictional+characters+Wonder+Woman&hl=en+as_sdt=2006
Twin Peaks Productions, Inc. v. Publications International, 996 F.2d 1366, Court of Appeals, 2nd Circuit, 1993:
http://scholar.google.com/scholar_case?case=1671961186681268324&q=copyrights+and+trademarks+in+fictional+characters&hl=en&as_sdt=2006
Walt Disney Productions v. Air Pirates, 581 F.2d 751, Court of Appeals, 9th Circuit, 1978:
http://scholar.google.com/scholar_case?case=12985824547460808287&q=copyrights+and+trademarks+in+literary+characters&hl=en&as_sdt=2006
