In past, I remember system always search name and lastname in this relation ...
Now system search only in field lastname ...
I don't think so, I'd say those popup searches have always worked only on one column.
If you are searching for a Potential or a Ticket on their Related To field, the search will be on first and last name, but if you are searching directly on the Contacts module (as you are doing in the above images) then you search on the field directly