No mixer channels can be renamed directly from the MIO Mixer window.
Renaming analog channels can be done in the MIO Console window, by double clicking the in/output name.
Renaming digital channels can be done in the MIO Console window, by double clicking the name under the drop down list after selecting the digital type (ADAT/TOS)
You can rename all channels (including DAW types) by using the Mixer Config utility found under the Mixer title bar menu.