I fear that there is some misunderstanding on the name "Aragon":
1) On one hand it refers to the geographical and historical region known as Aragón, which corresponds to the present-day region of Aragón and approx. to the EU province of Aragón.
2) On the other hand the generical name "kingdom of Aragón" is an oversimplification for the "commonwealth" formed by Aragón (in the first sense of (1)), Catalonia, Valencia, Mallorca and, during different years Sicily, Sardinia, Naples and Provence. When the "commonwealth" was formed by the union of the kingdom of Aragón and the county of Barcelona, the highest title was that of "kingdom" which Aragón had, while Barcelona was only a "county", hence the simplification of calling the country "kingdom of Aragón".