There's 2 big differences between FB and G+ in terms of real names.

First, FB is really lax about enforcing its policy. Everytime they've started killing accounts (for example when they tried to purge all fake women) there's a huge public outcry when they stop. Often because they always screw up and purge tons of valid accounts, like G+ is doing now.

Secondly, G+ is linked to all your other google services. If google suspends your account you could lose your mail, calendar, contacts, etc. The loss of a fake FB accounts is much less risky than the loss of a fake G+ account. According to the reports I've read google is being inconsistent in their punishments for fake users. In some cases only the G+ profile is disabled, in some cases the whole account is frozen or destroyed.

mod the ticketing system (or upgrade or replace, whatever) such that a ticket cannot be closed without sufficient documentation on the problem.

they've gotta write *something* in there, it's a good first step.

you can make as many required fields as you need to capture the information you want.

who was served (or maybe this is already the employee who opened the ticket)
what kind of problem was it
how was it resolved
etc.

if you aren't getting enough detail in one of the fields, replace it with a drop down list. better yet, replace it with a bad, incomplete drop down list and an "other" field. nothing encourages a geek to provide detailed feedback better than a list of incorrect choices.

don't bother trying to convince your employees to change their behavior. invent a robot to do it for you.