How to do Domain site name translation (DA module) I just want to translate site name to different language - so when users browse a domain in english they see English site name, and when they browse in polish for example, they see Polska nazwa strony.

I got all modules (Domain Access, i18n, Variable) and I had enabled two languages, checked variable (site name) in admin/config/regional/i18n/variable - but I can't translate the site name.

I try to translate it on admin/config/system/site-information page - different name for en patch and different for pl - no results, and on admin/structure/domain/view/X/config - also without any results.

Any idea how to menage to translate site name? Am I doing something wrong?

I have tried the Domain Variable module also already (as suggested in one of the answers), with no avail. I have read this nice article by Jose, but it just doesn't work on my site (Drupal 7.38, Domain Access 3.11 and latest version of the Variable module). I did set everything step by step, but I can't figure out what is going on and why this doesn't work.
The project page of the "Domain Access" module says:


  If you use the contributed i18n module suite, you should use the Domain Variable module instead of the provided Domain Configuration and Domain Settings modules.


Therefore, I think you should try the Domain Variable module, to check if it fixes you issue.