Ascanius is Latin for the Greek Askanios, deriving from a-skanios, the Dweller. As usual in Greek /
Roman mythology, Ascanius has different backgrounds, depending on the author, he is either the son of Priamos, king of Troy,or the son of
Aeneas, founder of Rome (and son of Priamos), or also the son of a certain Hippotion. The mother is usually a goddess or half-goddess.
P.S. It is hard to find this kind of thing just by using general etymological lexica, I went to the Etymologisch-symbolisch-mythologisches Real-Wörterbuch zum Handgebrauch für Bilderforscher, Archäologen und bildende Künstler by F. Nork, published Stuttgart 1843 which you will find online. It is in
German, of course, but even if you don't read
German, check out the title which is just fantastically long and complicated - and enjoy!