I actually got a minor in linguistics, so I can tell you the International Phonetic Alphabet's (IPA) transcription of Caska's name you're using:
[kʰæska] (How Starnum probably says it)
[kaska] (How a Japanese person would probably say it)
[æ] is the Near-Open Front Unrounded vowel, and it appears in English in words like "cat" [kæt], "bat" [bæt], "rat" [ɹæt], or as you've already said, "basket" [bæskɪt].
[a] is the Open Front Unrounded vowel, and it's a little bit harder to pin-point in English, because it doesn't appear that often. The most common example is in the word "hot" [hat] (
click here for example), but people in the west of the US, like me, usually say [hɑt] with an Open Back Unrounded vowel instead (which appears in words like "rot" [ɹɑt], "bot" [bɑt], and "stalk" [stɑkʰ]), so it's hard to show this example to people sometimes.
The other thing there is the [k] sound (called Voiceless Velar Stop) which I wrote with an aspiration [kʰ]. In English, words that begin with a [k] are aspirated, in that there's a little bit of air rushing out after pronouncing the [k] and before pronouncing the following vowel. But it's not aspirated if it appears elsewhere (hence why the second [k] wasn't aspirated). Although I'm not quite sure of this second rule I made up, it's probably not so universal; it's just that I don't hear it in the word "Caska".
Anyway, I agree with Starnum's reasoning on why Caska's name is most likely [kʰæska] or something closer to it, but I would need to know exactly where and when it comes from to conclude more precisely.
"Clearly my escape had not been anticipated, or my benevolent master would not have expended such efforts to prevent me from going. And if my departure displeased him, then that was a victory, however small, for me." - Raziel