When copying a model, specifically an assembly, you typically copy a specific number of the original parts and reuse some of the other parts. In many cases, the newly copied parts are supposed to have the same function as the original parts, e.g. a support beam wil still be a support beam, possibly with another shape or dimensions or whatever.
When parts are selected to be copied instead of reused, the initial Common Name of the original parts disappears. In an assembly with quite a lot of parts to be copied, it would be useful to allow the user to modify the initial Common Name instead of removing it, which makes it difficult to recognize the parts afterwards.