According to Porto Editora’s Infopédia the common noun alvalade comes from the Portuguese vala or valado, ultimately from the Latin vallare, or to defend with trenches, whereas the place name Alvalade, freguesia de Lisboa and Alvalade in Alentejo, comes from Arabic al balat, meaning plain as in flat ground. There are various places in Spain named Albalat, and the origin given here is the same, but they say al-balat means path; The Dicionario de la Real Academia Española says stone-paved path.
As a common noun alvalade appears not to be in use anymore. Priberam lists it as antigo (ancient), and Dicionário da Academia das Ciências de Lisboa does not list it at all. According to Infopédia alvalade means campo ou pátio murado (walled field or yard). This is pretty much meaning 2 of valado
1 Vala, sebe ou elevação de terra que cerca uma propriedade. (Trench or ditch, hedge or fence, embankment, surrounding a piece of land.)
2 Propriedade rústica cercada por vala, sebe ou elevação. (Piece of land so surrounded.)
Past participle of the verb valar (dig a trench in, surround with a trench). Related to vala (ditch, trench).
In Spanish there is the word balate, the meaning of which (embankment, slope, edge of a ditch) closely resembles meaning 1 of valado, and comes from Arabic al-balat.
So, my best guess is that in former times the two words, valado and alvalade, similar in meaning to begin with, merged their meanings, and then alvalade was forgotten as a common noun and survived as a place name only.
The name Alvalade in Lisbon appears to be very old, for the confrontation that took place there between King D. Dinis and the Crown Prince Afonso (future King D. Afonso IV) in 1323 is known as Battle de Alvalade. No battle took place though, thanks to the last-ditch conciliatory efforts by the wife and mother of the belligerents.