Boricua" goes back centuries. The island was called Boriken by the native Taínos. "Boricua" was derived from Boriken - most likely coined by early colonial Spaniards. All those names Boricua, Borinquen, Borincano, Borinqueño - are very old
Puerto Rican terminology found in old Puerto Rican
history books, and poems that are over 200 years old, etc. If you have not studied in
Puerto Rico and read these words in our own Spanish literature (in school textbooks) and native poems then you might think of them as "foreign" but they are not. You are right they are not "proper" Castellano, but only Spaniards speak "proper" Castellano. These terms are actually "criollo" - developed in the island. They are true Puerto Rican terminology.)