I guess every country has public-right or state-owned radio/TV. I've started a list with names of such broadcasters. Do you know of a country where public-right or state-owned radio/TV doesn't have a boring name?
RADIO
France: "Radio France"
with the stations "France 2" and "France 3", formerly "Antenne 2" and "France Régional 3"
Germany: "Deutschlandradio" [Germany Radio] / "Deutschlandfunk" [Germany Radio]
TV
France: "France Télévision"
with the stations "France 2" and "France 3"
Germany: "Zweites Deutsches Fernsehen" [Second German Television] ZDF
and, as the association combining the regional networks and its TV channel: "Arbeitsgemeinschaft der öffentlich-rechtlichen Rundfunkanstalten in Deutschland" [Association of the Public-Right Broadcasting Networks in Germany] ARD
Italy:
RAI
Spain: "Televisión Española" [Spanish Television] TVE
United States: "Public Broadcasting Service" PBS
RADIO & TV
Australia: "Australian Broadcasting Corporation" ABC
Austria: "Österreichischer Rundfunk" [Austrian Broadcasting] ORF
Bavaria: "Bayerischer Rundfunk" [Bavarian Broadcasting] BR
Berlin-Brandenburg: "Radio Berlin-Brandenburg" RBB
Bremen: "Radio Bremen" RB
Canada (English): "Canadian Broadcasting Corporation" CBC
Canada (French): "Radio Canada"
Central-Eastern Germany (SN, ST, TH): "Mitteldeutscher Rundfunk" [Central German Broadcasting] MDR
Germany (abroad): "Deutsche Welle" [German Wave] DW
Luxembourg: "Radio Télé Lëtzebuerg" [Radio Television Luxembourg] RTL
Hesse: "Hessischer Rundfunk" [Hessian Broadcasting] HR
Northern Germany (HH, NI, MV, SH): "Norddeutscher Rundfunk" [North German Broadcasting] NDR
North Rhine-Westphalia: "Westdeutscher Rundfunk" [West German Broadcasting] WDR
Saarland: "Saarländischer Rundfunk" [Saarlandian Broadcasting] SR
South-Western Germany (BW and RP): "Südwestrundfunk" [South-West Broadcasting] SWR
United Kingdom (and abroad): "British Broadcasting Corporation" BBC
The names of public-right radio stations are usually just the name of the broadcasting corporation plus a number, e.g. SWR 3.