You can remove the prefix with metamta.differential.subject-prefix, and remove the action with metamta.vary-subjects, but both of these will also affect mail.

It makes more sense to use the mail message title in Asana, as the integration is essentially replacing mail. It makes less sense to use it in JIRA, and the object's handle's full name is probably the right string to use. I think it's probably OK to just use that universally.

in Asana, does the title updates the ticket's title?

As I recall, yes. But the only install I'm aware of that uses it (Asana itself) also disables the mail prefix, and might disable subject variance, although I'm not sure.