I believe that in Klingon, "Hi, I'm Jim Miller" would be *Jim Miller jIH*
Correct. There's no "hi" or "hello" in Klingon.
and "Hello, my name is Kate Stewart" would be *Kate Stewart pongwIj*. Am I correct?
This would very probably be understood, and might even be accepted as correct "clipped Klingon", but the non-clipped, grammatically uncontroversial version would be: {Kate Stewart 'oH pongwIj'e'}.
I'm not aware of any examples of the pronoun and {-'e'} being dropped in a copula construction in clipped Klingon, except when the subject is a question word. ({Dochvam nuq} from Conversational Klingon looks like it is the clipped form of {Dochvam 'oH nuq'e'}, even though the grammar isn't explained explicitly.)
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De'vID