Please note that the customer on the ticket will be set as the original sender of the email - which may be taken from the address the form is generated from, rather than an email address of a customer within the body of the form.
There are two steps to work around this:
1. Make sure that the email with the form submission is forwarded to your Desk inbox from an email address of one of your agents. It may help to have the forms sent to an agent and for them to have a forwarding rule that sends them on to your inbox automatically.
2. Set the sender header "X-Original-Sender" to the address of the customer in your form.
Please note: If you are using third-party form builder, it might not be possible to change the sender header details, and some may do it automatically - please check with their support to find out.