This is just the exactly wrong way to go about it. When dealing with policies, you concern yourself with real world cases, and making sure that the policy works most of the time. You don’t put primary focus on the grey areas. Such will always exist.
That said, I your case isn’t all that hard. First you ask the kid to spell it, which would weed out those who didn’t think fast enough. If they spell it like a real name, you if they’re sure , because you will call them that for the rest of the year/semester/quarter. If they say yes, you call the kid Bodie. Maybe the class snickers. So what? A joke can only be funny for so long before people get tired of it, and kids get tired of it more quickly. And now the kid faces the consequences of their “joke,” being the one who gets made fun of for their “lame” name.
Furthermore, if you’re concerned about being sued, that makes it more obvious. The only suit that could possibly have merit would be a discrimination case against you. And that would only happen if you don’t use someone’s preferred name. Some kids snickering vs. you being sued: pretty easy answer.
I can’t agree that this is at all difficult. The vast majority of the time, it will be abundantly clear whether the name is legit or not. And, when you can’t, you err on the side of using the name they gave you.
(Of course, if there is a policy as in the OP, then it’s even easier, as the decision isn’t yours to make anyways, unless you want to quit. Use the name they gave, and then run it by whoever you’re supposed to discuss possible policy exceptions with.)