Your title should be your Current professional title. You can change your title as it pertains to the profession you are applying to but I would balance that with how laughable it sounds.
For instance if I wanted to switch careers to a role as a professional speed skater it would be appropriate to call myself:
Speed Skating Enthusiast
or
Amateur Speed Skater
It would definitely be inappropriate to call myself even:
Speed Skater
Because I am not and never have been.
Leaving a title off is never wrong. At worst you are missing a chance to say something (possibly positive) about yourself.
Using your old title is best unless it will raise huge red flags. A software engineer applying for a dishwasher job isn't likely to even get an interview with me. It just seems too incongruous. However a transition from Engineer to Academics doesn't come off as nearly as unintelligible.