It is not possible to get the field name that way. Get ( activefieldname ) returns the name of the field that currently has the "focus" (the cursor is in it for editing) and quick find does not drop the cursor into the field where the text was found.
I know of no simple way to produce the results that you want. In fact, the need to perform this kind of search in the first place (I'm not a big fan of quick find for this reason) creates questions in my mind as to why you need to perform such a search in the first place.
Say you have a record with a name field and a street address field. Doing quick find for "Smith", pulling up records where Smith is found in the name field and also in the street field seems a pretty pointless result. Normally, one wants records where the specified text is found in one field or the other but not both.
While you may not have a name field and an address field, one normally uses multiple fields in multiple tables as a way to segregate different types of data and thus such a "catholic" search would seem very likely to find records that are not useful to the user as the data might be found in either the wrong field and/or the wrong table than for what the user needed as a search result.