The Spanish La Liga is the equivalent to the English Premier League. That is the premier Spanish football league. In order to brand the product they have changed the name from LFP and to La Liga. LFP means Liga Futbol Profesional. La Liga is easier to remember and to comprehend thus it has probably been a smart move to change the name. All 20 clubs competing in La Liga wear the badge to the right arm sleeve whenever they play Spanish league matches.
Barcelona would typically have a sponsorlogo to the left arm sleeve. In the past it used to be TV3 , which is a Catalan broadcaster broadcasting in Catalan language. More recently the sponsor has been Beko, a Turkish brand of consumer hard goods like washing machines and kitchen appliances.
Real Madrid has so far shyed away from a sponsor logo to the left arm sleeve. They do not have a stadium sponsor yet either. But if the bid is high enough I guess that Florentino could be tempted……