I’m not looking for a contraction as in this sentence.
But ‘Going to the shop’ instead of ‘I’m going to the shop’.
I don’t know if there’s a specific name for excising ‘I am’, but it could be considered a conversational deletion.
Understood subject?
There’s a thing called an “elliptical construction,” in which you leave words out knowing the reader/listener will understand what you mean.
I would go with “situational ellipsis” or “subject ellipsis.”
ETA: See “situational ellipsis” here:
According to the Yale Grammatical Diversity Project, this is an example of “null copula”, or “copula deletion”, where the copular - connecting - verb “to be” is omitted. It’s a common feature of African-American Vernacular English, but it shows up in other English dialects, as well.
But the null copula, as defined in the link, keeps the subject intact. OP omitted it as well as the auxiliary verb. Does that make a difference?
It’s certainly an example of ellipsis, at least. Beyond that, just quibbling about details.
Been there, done that. Happens all the time. No worries. Gone fishin.’ Feels bad, man.
My instinct says “no”. But then, I’m not a linguist.