@AK47 maybe this is too obvious... I don't work with parent customers, but I work with parent items (so item search), and maybe it's similar. One I've used when a child field is blank, pull the parent version of the field. I do this in the "Results" tab of the saved search, set the field to Formula (text) then do a formula that does something like this:
CASE WHEN ({custfieldID} is NULL) THEN {Parent.custfieldID} ELSE {custfieldID} END
Then set the "Custom Label" field to whatever title is appropriate. This works for me... Unless both are blank, then that's another issue 😉
Maybe that will help?