Well, I can not tell you why the name of Reyes has been inherited generation after generation, but I can get a rough idea of why there is this name in your family, starting with the surname Arellano:
The Arellano is a family of Basque-Navarre in Estella (Euskadi, Spain) is its trunk Sancho Ramírez (grandfather) who was King of Aragon and Pamplona, the father of Ramiro Sánchez de Pamplona, who in turn was the father of Don Sancho Ramirez (grandson) and Don Garcia Ramirez "The Restorer" King of Navarre. García Ramírez the Restorer married Elvira Gómez (daughter of Count Gomez Gonzalez Saviors and his wife Urraca Diaz's house Ansurez).
From this union was born Sancho Sanchez, first Lord of the Villa de Arellano, taking on the last name that place. The family of Arellano passed to the kingdom of Castilla and León and then to America, founding new home in Mexico. Today descendants can be found throughout Spain and Latin America, namely Mexico, Chile, Colombia, Peru and Venezuela.
Juan Ramirez Arellano, Lord of Arellano, received the Lordship of Cameros to help King Henry II of Castile after the Battle of Najera, who was part of the Hundred Years War.
By the year 1475, the Catholic Monarchs granted the title of Count of Aguilar de Hinestrillas to Don Alonso Ramírez Arellano, sixth Lord of Cameros. Don Alonso Ramírez Arellano was the first Count of Aguilar. From this branch descends Don Diego Ramirez Arellano, marine and geographer who took part in the Nodal brothers expeditions to the Strait of Magellan and was the discoverer of the islands that even now bear his name.
Well this is all I know, it could be that the name of Reyes comes from the origins of the Arellano family.