I agree 100% with @Mike McCarthy - if your tenant stops paying, there is no magical way for your new PM to get them to pay up. I just would hate for you to pay for this PM and end up disappointed, and also take it out on the PM when they're charging you management fees and you're not getting rents.
Other than that, vet the PMs you talk to not only on their rent collection/enforcement and eviction processes and how updated you will be, but also on their rent-ready process, marketing/showings procedure, and tenant screening criteria. Be clear on all fees that may apply.
Once you're ready to take that step, make sure you know when the PM will reach out to your tenant, and give them a very simple heads up first. "Hello, I have hired a property management company. All future correspondence and payments need to go to them. Their name is _____ and they'll be contacting you soon." The key is after this - you should no longer correspond with your tenants. If they are really trying to be manipulative, they will likely try to go straight to you and you will just need to report any such communications to the PM and not respond (unless there's truly an emergency, of course).
One word of advice - never schedule the change to occur right before rent is due. So if you're planning to have your new PM responsible for collecting Nov rent on Nov 1, you need to act fast so as not to have this introduction happening in the last few days of October.