Domain Access + Domain i18n = Site names not translating in other languages?
I'm assuming you're using the "Domain Access" module. And even though you didn't explicitely mention it, you also use the i18n module. If my assumptions are correct, then be aware of what's mentioned on the project page of the "Domain Access" module:


  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.


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