Edited
ArcGIS Pro 3.1
When I copy/paste an FC into the same geodatabase, Catalog avoids creating a duplicate by adding "_1" as a suffix to the FC.

To me, I think it would make more sense to start the numbering at _2, not _1. Since there already is a "1" version of the FC -- the original.
Otherwise, I find I'm always going back and renaming _1 to _2. That seems like an unnecessary step.