What does it mean when it´s placed at the end of someone´s name?

Thanks in advance.

Zehra´cığım example

It is like my dear Zehra..

 It is a combination of the cik/cuk suffix + the im/um possessive suffix, generally meaning "my little ..., my dear ....." and used as a term of endearment.

See this post, in particular the 3rd response

So Ayşe + cik = Ayşecik (dear little Ayşe)

Ayşe + cik + im = Ayşeciğim (my dear little Ayşe), and often in text or colloquial language it may be written as Ayşecim

Further examples are karıcığım (my dear wife), kocacığım (my dear husband), teyzeceğim (my dearest auntie)