The best method for me is to write out the morse sequence you're expecting, then listen to several iterations to get your ear in. Once you're locked into it, you get it no trouble. The skill is in hearing it automatically without knowing what it was and I've never done enough morse work to get it like that - I can pick out some letters, then listen again to pick out the others around it.
Some easy ones to listen out for in the chittering are R (dit dah dit) K (dah dit dah) and C (dah dit dah dit) because of the way the UA audio comes out - ordinarily you'd listen for things like S (dit dit dit) but the variance in tone and dot/dash length throws me.
In test area 2, the section labelled "WARKUSHANUI 1 A Star" produces chittering of WARKUSHANUI A in morse (no numeral).
EDIT: Listen to "WARKUSHANUI A 2" in test area 2. Once the main part of the name is done, there's a pause, then a clear dit dah (A), then another pause, then a really clear dit dit dah dah dah (2).
I'm asking myself right now if the chittering is staying the same in all 5 minutes, when the artifact is sending. I'm still thinking about what kind of message the name of a stellar object could possibly be.