The Reservations: Email module is what allows you to send eMails. Some more details about it (from its project page):
This module extends Reservations to send emails at different stages in the reservation process. Token based templates are included so the emails can be customized with any information from the Reservation node or User objects. Also included is a pseudo-token for a confirmation link that allows users to confirm reservations without the need to grant them the permission to confirm reservations.
However, looking at the module source, using tokens in the eMail body requires that the token module is enabled. So if you haven't enabled that module yet, it may explain why you "could not find a token to use to refer to the user in the email body" (as in your question).
About your extra comment like "... I had to add a new field to the reservation type to save the name of the user requesting the resource. I later used that field in the email.": that seems like a variation of what's written in the issue about "Sending emails to anonymous users". That issue contains a patch that you may want to look at also.