My English and I are from the UK; US English often works differently.
…in a relationship with… Duo's short sentence "Adam jest w związku z Martą" is most closely translated by
- "Adam is in a relationship with Marta", which clearly indicates that
- "Adam and Marta are a couple", as the broader
- "Adam and Marta have a relationship" might or might not imply – this could instead be a business or working relationship, perhaps.
- "Something's going on between Adam and Marta" might imply all of the above, or even that they're in the same orchestra or criminal gang…
It's safest to learn "A is in a relationship with B" as a set English expression. Generally I encourage language learners to use clear expressions that avoid ambiguity and embarrassment, but if you want to muddy your meaning, leave out a and try
…in relationship with… – which might mean relative to; with respect to.
- "Adam is in relationship with Marta" doesn't work in (UK) English, though
- "Adam is in partnership with Marta" (i.e. business relationship) is fine.
It's difficult to find good constructions that work without a, suggesting that it's very much minority usage, but try…
- "Adam was in relationship with 8 other women before he finally met Marta."
(here I prefer …in relationships with… to hint that many of the relationships may have been at different times)
- "People tend to behave differently in isolation or in relationship with other people."
- "In a car engine, any single part has to function correctly in relationship with thousands of others."
- "Company A is in relationship with Company B." [?US usage]
Batman vs Superman? :)
"imię" is a neuter noun. The right form is "tamtego imienia", but it sounds like 'that name over there', so I'd definitely say "tego imienia" even if that's literally "this name".
And as for "używał", it does make sense, but it's for 'using multiple times', so "użył" (on a specific occasion) is better. We arrive at "Dlaczego użył tego imienia?!".