Hmm, I would do what CrochetGal does but if you are also in a time crunch and they haven't responded, I would just add wording in your policies that you will print the names as given and that it's up to the customer to proof their names before it ships. Or something like that.
When I did "from santa" tags in my old shop, I didn't proof them before they shipped out, I just would ship them based on the names given. If the customer doesn't get back to you, just assume that they gave you the names correct and word your policies to protect yourself.