Character name (and title if enabled) and if cross-realm you get " - RealmName"
example " Realms Worst Hunter Manyshots - BurningBlade" {Title and name fictitious.. realm name valid

My question for you is.. have you any information of other handling of realm names in the tool tip? What you see there is what I can get from the game api calls used in the addon. Unfortunately I expect the only way you will see these realm names is when you are in cross-realm battlegrounds, so you need to be on a server in the same battlegroup. US realms may be able to get this from cross-realm zones.. which apparently isn't yet implemented in EU region.
[Edit].. oh wait.. I forgot the Looking for Dungeon group tool that is also cross realm.
how do these realms show up?
"Azjol-Nerub"
"Blade's Edge"
"The Venture Co"
and really how do these realms show up? (I can only see the names as provided by Blizzard realm status pages.) If they do show as different names for the same realm, I'll need to trap and change the realm names.
EU realms
"Die Arguswacht" a German RP-PVP realm which I believe is called "La Veille d'Argus" only when using the French language pack.
"Scarshield Legion" an English RP-PVP realm which I believe is called "Légion du Bouclier balafré" only when using the French language pack.
US realms
"Nemesis" a Brazilian PVP realm which shows up only in the es_MX Spanish language as "Némesis"
and last but not least how about:
"Pozzo dell'Eternità" the Italian PVE realm which shows up as that when using Italian language everywhere else it is "Well of Eternity"