Terminology Question-Verb that (inflects?) for emotional attachment

Good evening, everyone!

Although I've been developing my conlang for about seven years now, I don't
have a strong grasp of the correct terminology to describe my grammar.
There is one aspect of Angosian grammar in particular that I don't know how
to describe.  It developed about four years ago, and has been a feature of
the language ever since.

The feature in question is a suffix on the verb that denotes emotional
involvement with the subject being discussed.  For lack of a better term,
I've been calling it the passionate/emotive tense/mood.

For example:

Emzira   (observational tense/mood)

Emziraya (emotive tense/mood)

So to say "I see a cat," you would probably use the observational mood*:

Emzira al kata.

*Unless your cat had been lost for weeks and presumed dead and you were
immensely relieved to have it back

But to say "I see the love of my life" you would most likely use the emotive
mood:

Emziraya al emezakayrye.

Note that the emotive mood/tense depends on the perspective of the speaker.

So what should I call this "passionate/emotive tense/mood" if I ever write
this language up for the outside world?  And are there any natural languages
that have similar features?

-Danny