In books from 200 years ago, persons of full or partial African descent were called negros, blacks, or niggers. They all meant pretty much the same thing.

At some point, blacks decided that "niggers" was offensive. Perhaps because it didn't seem as "proper" a word as "negro". But bigots started associating the word "negro" with bad things. So some blacks decided that they ought to use the word "colored" instead. And the bigots started associating the word "colored" with bad things. So some blacks started insisting that they should be called "Afro-American". And the bigots really had a good time laughing at that, and piled extra scorn on the term, and associated it with all the negative things they always did, but adding cowardice and deception to the list - because in the minds of the bigots, this was proof that black people were trying to run or hide from who they really were. After that "blacks" was the accepted term, and for the first time in a long time was actually one of the original words used. About that time, black people made very significant gains in legal and social equality. Since then, some hypersensitive folk have insisted on "African-American", but blacks themselves have resisted yet another name change, especially one which they don't really relate to - and in any case, black people aren't stupid. They know who treats them fairly and who doesn't, regardless of what words they use.

Most recently, "nigga" is the preferred use in some parts of the black community, where some have decided to turn the old epithet into a mark of pride.

But the point of all this is: it didn't matter much what term was used. Bigots remained bigots because they were stupid or hateful or willfully ignorant, not because one term or another was in common use.

On the other hand, it must be said that having new terms did at least allow those whites who wanted to distance themselves from bigotry to do so in a simple and public way.

It can be useful to have multiple terms, especially when they have different shades of meaning. The important thing, however, is to address the issues of ignorance and hatred. If that can be done, what we call ourselves won't matter so much.