"Hello, I am Nur."
Translation:Merhaba, ben Nur.
No one would introduce herself as "Ben Nur'um" under normal circumstances.
You would go up to someone and say: "Merhaba, ben Nur. Siz?" and the other person would go: "Merhaba, ben de Cem." (Never "Ben de Cem'im".)
Nur'um/Cem'im could only happen when someone confuses your name with something else. Like:
Pınar, listede yazılana göre, sana bu görev verilmiş. Niye yapmadın? (Pınar, according to what's on this list, you've been assigned to this job. Why didn't you do it?)
İyi de, ben Nur'um. (But, I'm Nur.)