As I have just read, Complutense is a traditional gentilice for the comune of Alcalá de Henares in the grand area of Madrid, which in Roman times was called Complutum. Towards the end of the XIXth century and beginning of the XXth century, the University of Alcalá de Henares was the only one authorized to issue doctoral titles, and so, the University of Madrid became associated with the University of Alcalá and gained that epithome.