As a similar sentence with Julia (Jestem z Julią) made clear to me, women's names to decline (change according to grammatical role). If Polish is like other declined languages, this may only apply to foreign names when it is clear how they would decline. I would be interested to hear from a Polish person how she would deal with a name like Sue (Susan wouldn't be too hard, though).
Sometimes with male names such 'e' vanishes as here. And sometimes you just end -em without any other changes. With a name you don't know, it's possible that you won't be sure what the basic version is.
Another thing about this specific sentence and specific name: the writing doesn't tell us anything about whether this is a Polish guy named "Jacek" or an English/American guy called "Jack". Only pronunciation would tell us that: Polish "Jestem z Jackiem" vs English "Jestem z Dżekiem".