Hi everybody, my name's Gustavo Alday, and i'm from The Basque Country (in the north of Spain). Well, I must say that Alday surname is original from Basque Country natives. This is a millenary people that has had very little contact with other people. Many centuries ago they sailed all over the world,England, South America, and North America. So, what I mean is that probably original Basque Alday converted to Allday somewhere in England or USA. Most South American Alday's are direct descendents from Basque people who travelled there.
I'm sure that all i'm telling you can be proved in some way, i think i've given you a new start point to search for additional info.