In what cases is it ok to remove a name from a safe deposit box? We have a customer getting divorced and has requested his wife's name be removed from the box.

I would not -I would give him the option of closing Box 1 and opening Box 2- keep the bank out of customer's personal issues. Too many potential pitfalls to the scenario you describe.

Ask the customer to surrender the box and rent him another one. He does not have the right to remove another person's name from the SDB contract.

That is the only way we do it. As long as it isn't a 2 signature requirement then any one owner has the right to close it. And they can open a new one in just their name. If it is a 2 signature box, then you have a different issue and she would have to sign.

Everyone do the same on joint accounts when a divorce is involved?

Yes. We close and reopen a new account. It doesn't keep the bank completely out of the middle of a disasterous situation but it helps.