Translate Label names

Is it possible to translate the variable label names to the different languages that I have installed on my site.

Yes, use a language key for your labels then use a language override against that language key. Example as follows.

Key: PROFILE_FIELD_ADDRESS
String: Address

With the above you'd set your fields label parameter PROFILE_FIELD_ADDRESS. See the below on how to use language overrides within CB.

www.joomlapolis.com/blog/kyle/18701-language-overrides-have-arrived

is Key the same as Field Name?

I have make a text field with name cb_profilheadline and the label is About me
How I make translation of this?

You translate the Title parameter. Not the Name parameter. Edit your field within CB > Field Management and find out what Title is set to. You can then override that in your language files to translate it using the language overrides functionality linked above. Example as follows.

Field
Title: PROFILE_FIELD_ABOUT_ME

Language Override
Key: PROFILE_FIELD_ABOUT_ME
String: About Me