Yes: As pointed out in the question, "Real" in this case means "Royal". It is, somehow, a honorary title. There are quite a few Spanish football teams with "Real" in their names, and in fact you have a specific (Spanish) Wikipedia category: Equipos de fútbol de España con título Real. read more
In Spanish, "Real" means "Royal". The king Alfonso XIII of Spain was fond of football and became the patron of many football clubs, which led to these clubs adding the name "Real" to indicate the royal patronage they received. PS- all these clubs have a crown in their crest to indicate this. read more
The word 'Real' means 'Royal' in Spanish, but it also means 'Kingly'. Most of these clubs that prefix their name with Real enjoy the patronage of. read more