Is it permissible to be named "Salih" (righteous) because it carries a commendation of oneself, and can references for the meanings of names and sources for purchasing them be indicated?

It is permissible to be named "Saleh" because it is one of the proper names and names of prophets. As Sheikh Ibn Uthaymeen said, there is no harm in names that imply commendation when they are used merely as proper nouns. The prohibition against names that imply commendation is for a milder dislike (tanzih) rather than outright prohibition (tahrim).