One of the biggest and most destructive mistakes that any manager can make is to let an employee think of any Customer as 'theirs'. They can certainly take ownership of a Customer's needs and issues, but not the Customer, ever. The Customer belongs to the business, not to the employee, no matter how terrific they are.
The only thing that stops you from putting this into practice is fear. But is that really how you want to run your business, doing anything to keep employees and Customers? Because if you do, it's not your business any more, no matter who signs the checks.
"Nonsense!" you say. "What harm can allowing an employee to bond with a Customer cause? So what if they do things outside of our established process - they bring in results!"
What you're missing is that it's just another version of the 'special situation'. If you allow one employee to work outside of what is normally allowed, it creates extra work for everyone involved down the chain, and breeds resentment among the employees that are not so privileged. It's likely that your star player is only a star because they're allowed to circumvent the rules. But if that's true, why not do away with the rules entirely and let everyone do what they want with 'their' Customers?
Because you fought long and hard to get away from that chaos - remember? - and now you're backsliding.
"But it builds employee loyalty!"
Nonsense. What it breeds are bullies who make life hell for everyone else when they don't get their way, setting impossible Customer expectations that cost your organization time, money, and yes, Customers. And if Customers know that they can get whatever they want by going to your bully, why would any of them go to anyone else?
And then, of course, your bully leaves, and takes all of 'their' Customers with them, while you curse them for being exactly what you made them.
Stop being co-dependent! If there are rules, they apply to everyone, and anyone who can't succeed by following them doesn't belong. Stop allowing employees to run your business - that's your job. If you don't do it, nature abhors a vacuum, and is more than willing to put someone else in your chair, whether you realize it or not.