How is at called when a person can't feel the sense of recognition? I meet a person who doesn't feel a sense of recognition. When for example forgetting a name, and you give them a few choices, they can tell you whether one of the choices feels "right" through a corresponding bodily sensation.

How is it called when a person can't feel such a sense of recognition?
There are several conditions associated with a disconnect between the feeling of recognizing something, the ability to name something, the ability to react to something appropriately, etc. called agnosias.

https://en.wikipedia.org/wiki/Agnosia

EDIT: See also "capgras delusion", which is possibly a more extreme version of what you're describing.

https://en.wikipedia.org/wiki/Capgras_delusion