Can a person's name be used to represent a group of people?
Can a name of a person (usually from stories, or history) be used to describe a group of people? For example, can Cinderella be used to refer to girls who are poor and have difficulties in life, but who are then lucky to marry a wonderful husband?
Also, are there any more examples like this in the American culture?
Solution 1:
A fictional character can be recognised as an archetype and the name of the character comes to represent the set of people who exhibit its principal features. An example of this is Polyanna, the eternal optimist who always sees the positive in things.
The novel's success brought the term "Pollyanna" (along with the adjective "pollyannaish" and the noun "Pollyannaism") into the language to describe someone who seems always to be able to find something to be "glad" about no matter what circumstances arise. It is sometimes used pejoratively, referring to someone whose optimism is excessive to the point of naïveté or refusing to accept the facts of an unfortunate situation.
Solution 2:
I'll say it is valid to do so.
You can use this as an adjective or a common noun - but you need to be sure whether those who hear you or read this understand what you mean by Cinderella.
If you say "She's a Cinderella", then it means "fairy-tale" ending but I could also say "Cinderella (curfew)" to mean she has to be home by midnight. Another example would be Romeo, it could mean a guy besotted in love but does it also imply a tragic ending?
I can find a valid i.e. dictionary example with the word shylock which is a Shakespearean character and has the derived meaning "A ruthless moneylender; a loan shark" from the character (though it can have unintended negative connotations).
I also see sherlock can be used as a term for private detectives.
Other examples could be calling someone a Barbie(warning: it's trademarked) instead of dumb blonde or a JLo (I'll leave you to work it out)
Of course there are eponyms which is where the name of a person i.e. a proper noun has become the name of a product or place or thing. Words such as atlas, Victorian (era), Alzheimer's (disease) , Atkins (diet), Oedipus (complex) but I don't think that's the usage you're looking for.
Solution 3:
Can a person's name be used to represent a group of people?
Not quite from the stories, but sometimes the first name can be used generically to refer to anyone ('average Joe') or stereotypes for ethnicity (for example Ivan for a Russian).
Another clear example of fictional name becoming common word is Lolita:
a precociously seductive girl
from Lolita, character in the novel Lolita (1955) by Vladimir Nabokov