Just a thought about this one: I don't think you could do this with the name field itself, since the job names are set as soon as a job is created (before the AOI is even assigned, I would guess).
However, that said... instead of using the job name field for your application, could you use an extended property field instead? You can set extended properties at any time, and it should be pretty straightforward to set up a model or script that populates an extended property based on your AOI or some attribute of a specific feature. And you could obviously make the value look like a job name.
I hope that helps.