Just confirming ...
That you are referring to, a "Name" 'Tag', NOT, a "Topic" 'Tag'.
As, they are different.
"Name" 'Tags' associate the "Memory" with the individual/person.
[ A "Name" 'Tage' can ONLY be associated with ONE individual/person ]
Whereas, "Topic" 'Tags' are for "Searching".
[ More than one individual/person can have the same "Topic" 'Tag'. ]
There are 2 parts of a memory tag
the “tag name” & if known the FamilySearch ID associated with the person
if you create a Tag for John Smith, but do not link it to a specific FamilySearch ID it will not show on any person’s memories page