Renaming portions of a clip

Hi everyone,
I've filmed an interview in one long clip - approximately 2 hours long. Now I'm editing it, and for the purpose of organization (very necessary for my project), I went through and spliced my one clip into separate clips in the timeline. I dragged the smaller clips back into the browser, and renamed them without trouble. But now, I need to rename portions of these already divided portions of my original long clip, and it won't work. When I splice my clip titled "intro" into two parts, when I drag one part back into the browser and rename, both parts get renamed. Is there any sort of work around for this? Why was I able to rename portions of the big clip on the first round, but now cannot rename portions of the portions of the big clip? Would nesting the clips be a viable solution? I considered this possibility but I do not know if that results in any quality degradation. Any help anybody can offer is much appreciated!

Thanks,

Zachary Silver