The general naming practice, it is only a named chalice if purchased with name. If lineage can not be traced. It is a no name even if it looks like it had one.
Only a small portion of chalices fragged are named. Many LFS may give a piece they bought a name, but that same piece can be at another place. They gave it a different name. Neither names are considered a nationally none named chalice.
Your first chalice looks like it could be a echinophyllia maybe the aspera variety. The second is a bit harder to tell the chalice class. Many chalices look alike and hard to actually tell the species type.