Yes the Mk1 tuner does allow you to set the station name. It will even get it for you automatically if the station transmits RDS text. You can of course give the station preset a different name to the one transmitted (well I'm pretty sure you can - it's a while since I used my Mk1). The station frequency is displayed, as is the preset number, any live RDS text being transmitted my the station, and of course the station name. I thought the radio display on the Mk1 was pretty good actually!

(list 6284, Mk1 S/N 00299 4GB blue [for sale]. Mk2 S/N 080000094 6GB blue)