I have installed Domain Access, Domain Variable, Variable + i18n integration, etc. I have been able to change the value of site_lema for different domains and languages, but I cannot override the value of site_name, which is taken, apparently, from the Domain Access human readable name. I don't understand if that is a limitation, if I have something wrong in my Drupal (I have tested in two different installations), or there is some conflict with other module? Someone has achieved to have site_name changed for every possible domain/language combination?
It seems that the option in Domain Access "Override site name with name of domain." was causing all the problems. It was so simple, but was driving me crazy. It was checked and thus if I tried to change the value elsewhere (in the Variables section or in the Site info section), nothing happened, the value was not changed. Unchecking this option ("Override site name...") in the Domain Access configuration, this variable "site_name" can have multiple values depending on language and domain combinations.