In Desktop you setup shares. The name displayed on the TiVo is the name of the share.I believe this name was a configuration option in pyTivo in the pytivo.conf file. I haven't installed pyTiVo Desktop yet so not sure of the best way to configure it this with Dan's version.
[Now Playing on HERRONWHS]
FYI, regarding your disappearing issue. I haven't had that issue here with TiVo Desktop and Windows 10 using Bonjour except when the PC is configured for sleep mode (I disabled that for my laptop when plugged into AC power).