I pruned my resume and list of references, and in lieu of that I contacted HR at those locations and had them make a note in my employee file. I also had my transcripts updated at every school I went to, so they have my current name.
Most of the stuff on my resume, I'm still friends with or in touch with those employers. They are all aware of my transition. The few people I've chosen as references are all aware that they are listed as references and that I don't want to be out to potential employers.
It really depends on the kinds of places you used to work at. Most of mine were big places, and instead of calling an individual manager as a "reference", a potential employer calls HR to see if I was employed there, how long, why I left, and if there were any disciplinary issues.
At a smaller employer or small business, that HR function may fall to the owner or a manager. I'd say either get in touch with them and let them know, or worst case scenario remove them from your resume. If there's no background check, there's no need to list all of your experience on your resume.