What do your shop policies state regarding custom orders? Now would be a great time to solidify those. If I were your customer, I would probably ask the same thing she's asking but I'd say, "Is there anything you can do for me?" Free shipping or a percent discount on the second order would make me happy, especially since custom orders are generally not return/refundable.
Bottom line though, it's her bad for buying something without having the name correct in the first place! I guess, as a shop owner, I would do my best to make her happy but also not be taken advantage of. I'd offer free shipping on the second order or, like Jenni suggested, replace it and have HER pay shipping if the name is common enough to list as a ready to ship item in your shop.