I have multiple categories and in some of them i need to put 2 or more identical categories (in name) in different parts of the site (under different categories).
Is there an option to redirect from one category to another category ?

(example: when user click on cat x under category y - will be directed to cat x under cat Z).

In K2 no.
You can use htaccess redirection or a 3rd party extension.

I'm not sure if I want to deal with htaccess.
Do you know about any 3rd party extension ?
(I use redirect extension but It's only apply to articles and does not work in categories)

@eran

You can use the core Redirect Joomla component to set up your redirects.