I think this situation is similar to Romania or Hungary. Obviously the recognized alternative names and the official names don't have an equal status. But the alternative name gained some degree of "officialty" by the governmental recognition. Békéšska Čaba is more similar to an official name than - for example - Päťkostolie but didn't became an equal alternative for Békéscsaba. You are right that these names are "weaker" than German names in Südtirol but "stronger" than not recognized minority names. Because of their transitional status or quasi-officiality I know that there good arguments against/for their usage. In Hungary I decided to change the infoboxes and no Hungarian user opposed this movement (I announced it on the noticeboard), so I think it is OK. In Romania Ronline and Dahn did the same, an edit war broke out but the majority of Romanian users accepted the new infoboxes. Obviously I would like to change the infoboxes of Southern Slovakia (according to the 20 % limit you wrote) but not at the expense of a major edit war.