Looks to me like a case of many compounding effects.
Firstly, Mala vs Malka. Polish WP entry (and the English one for that matter) both signify that her formal name was Malka Zimetbaum, but she was known as Mala. In this case, the SS used the formal name in a telegram about her while the article has chosen the more friendly method of referring to her.
Secondly, Edward vs Eduard. As both the Polish and English WP's use Edward Galiński (note the apostrophy on the 'n' in his last name), I believe that his first name (common name in many languages) was Germanized to "Eduard". Hence, both in Polish and English he is referred to as Edward Galiński while the SS Germanized his name into Eduard. His "known by" was Edek which is how Malka referred to him as illustrated by the citations both on the Polish and German WP entries (no citations on the English one).
The "Germanized" form means that the word was taken through the process of Germanization to make it suit the rules of the German language (Eindeutschung). In English, this happens to names as well (such as the Portuguese "Joao" known as "John" to most).
Hence, the 'correct' way to refer to them would be:
- Malka Zimetbaum, or Mala;
- Edward Galiński, or Edek.
If you were taken in by their story, you should perhaps prefer the latter forms which would have been the ones used by friends, lovers, etc...