First off, congratulations on being offered this customised order (or Commande speciale, in Paris term).
No deposit would be charged in the past until you confirmed the order (after you discussed with the designer, ala Ms Couli Jobert, viewed and tried the mock-up). 50% deposit would be charged when you confirmed the order. Then an agreement would be entered into between the customer and Hermes. Basically, the contract terms restrict Hermes from making the same bag to another customer without your consent. The lead time (from the first meeting with the designer, trying on mock up, to final delivery) could take 2 years or more.
Nowadays, the above does not hold true. As Periogirl28 has rightly pointed out, Hermes will first discuss with you about your design, but will only prepare sketch and do a mock up until 10% deposit is paid. I do not know how much deposit will be charged when the order is confirmed, but my wild guess is 40% on top of the 10% already paid. And the remaining balance to be paid when the bag is done.
You can also prepare your own drawing and design and pass to Hermes. The design department will then assess (if it is handsome enough for Hermes to make it) and provide a quote. If you go to this route, you will not have the opportunity to meet with Ms. Jobert and discuss the design, which is part of the fun of this special project. right?
Good luck and enjoy the C.S. project and you can have the bag named after your last name.