The names you mentioned above, Seville, Guadalajara, Granada, and Alcala de Henares are not the actual Arabic names of those places, but rather, are the Hispanicized versions of the Arabic names. In fact, some of the Arabic names are the Arabized versions of their Latin names. We can go even further, and say the some those Latin names are Latinized versions of previous versions.

For example, Sevilla is Ishbiliya in Arabic, which is an Arabized name of the previous version. Guadalajara is Wadi al-Hajara in Arabic, or the stone valley. Granada is Ghirnata.

In a sense, the Spanish Hispanicized the names of the cities they conquered, as much as the Muslims had Arabized the names of the cities they conquered.

Furthermore, the hundreds of years of Muslim presence had a profound impact on the Spanish language, and so the carrying over of city names was not a seen as a problem. On top of that, the cities formerly controlled by the Muslims had many Christians, and some Muslim inhabitants who stayed put, and who still called their cities what they had before the conquests.

The expulsion of the Moriscos from Iberia that might have served as a catalyst to Hispanicize the names of these cities only occurred well after the completion of the Reconquista, by which time the names had stuck.