I don't at all think Christians thought the word "Christian" was so bad that they had to hide it or replace it with something else. Neither do I think the word "universal," or "catholic," had a bad connotation for them.
The idea that Christian association with the state, or universal Christian unity, or Christian organization, is a bad thing came from the evolution of separatist groups who disliked associating Christianity with flawed political systems. They wanted to operate without the taint of working under authorities who were flawed and sometimes oppressive.
Christians sometimes don't wish to be associated with any form of organized "Christianity" if they think that form of Christianity is corrupt. So they don't necessarily dislike the word "Christianity" but wish to distance themselves from what they see as a jaded form of Christianity.
There is a group that I consider a "Christian cult" today who does not wish to be identified with the name of any particular Christian denomination. I think we make more of names than we should, and are sometimes too perfectionist in our wish to be "spiritually pure." We can "come out from among them" spiritually without living on an island.
But certain groups need to be more distinguished by their practices and beliefs than by their *names.* Otherwise, we get confused, and in the world the word "Christian," or "Christianity," begins to be associated with something that by default is evil and corrupt.
That is how many of the separatist Christian tradition now view much of historic Christianity, as corrupt because it was allied with either the Christian State or Catholicism. Some Christian states may be corrupt today, and a Catholic Pope or the Catholic Church may be somewhat corrupt today. But that doesn't mean these things are corrupt in all ways or were such in all times.
The richness of Christianity is such that it finds a way to express itself everywhere in many ways. Sometimes it ends up being misrepresented in corrupt forms. But Christianity itself is an expression of the perfect Christ, and we need to not throw out the baby with the bathwater.
Though some wish to malign us and insult us using terms of insult, we can use their "half truths" to show the power of Christ in our lives. We are indeed "little Christs" in a way, and as such, can freely adopt the term with pride. :)