That's going to happen because the same clip (from the bin) is being used for each time-line paste.
Right-click the clip in the bin and COPY. Then right-click PASTE CLIP...as many times as you will need it. Dupes will appear, each with a different number.
Drop each uniquely numbered clip into the time line where you want it, then click a clip to change its text. Only that clip will be affected.