As a cub becoming a Cliath during gameplay, who selects the Deed Name for the character within the game world? I've only seen one instance of this brought up in the novels and that takes place at a Rite of Acknowledgement after the Deed Name has already been selected. Is there any canon on this at all?
The only canon source I found so far is in the old Tribebook of the Stargazers (Sidebar: Choosing your name). Once a werewolf joins the Tribe they choose a new name and one is given them. The first part of the name is chosen by them themselves and is generally a source of inspiration, someone he feels to have a deep connection to. The second name comes from Chimera herself. She sends a descriptive statement which becomes the second name.
The second name you are referring to is called a "deed name" and all garou tribes have them. They are given to a garou to mark an achievement of some sort, hence the term. Different tribes and septs have different traditions, but generally they are given by a galliard. Garou can receive more than one deed name in their lifetime; in this case most often the new deed name will replace the old one, but you can also have more than one deed name. Most often a garou's first deed name is given to them around the time they pass their initiation and go from being a cub (rank 0) to a cliath (rank 1) but some go without being given a deed name for longer. You have to earn them, they cannot be chosen by yourself. The deed name is given to reflect something the garou has done or to describe a strength they have. On the flip side of this, a garou might be given a "scorn name" which is a mark of shame for some dishonorable trait or action. Scorn names are usually given by a ragabash.
I've asked one friend of mine that knows a lot of World of Darkness, and she told me that there's no specific garou that gives the deed name, it depends on the pack. Also she told me that there's no need to be a galliard or a ragabash to put a name, but it's so common. In my opinion, if it's a deed name, it's likely to be given by the talesinger (I've been searching some info), just because he/she is the most qualified to do so.