Warcraft III lore question regarding Arthas Menethil's name

I am curious how Arthas was called in Warcraft III.

Was his surname already Menethil or did Blizzard add this in WoW?

As far as I know the surname was never named but my colleague said otherwise.

Furthermore was the city Menethil in any way mentioned in Warcraft III? For example on the loading screen maps? I can't find any resemblance of that name.

According to the Quotes of Warcraft III the name "Menethil" was never mentioned. It seems they added in the name with World of Warcraft.

In WoW you can find the royal tomb of King Teneras Menethil II in Undercity (just above the Elevators). The inscription says.

Here lies King Terenas Menethil II -- Last True King of Lordaeron.

Great were his deeds -- long was his reign -- unthinkable was his death.

"May the Father lie blameless for the deeds of the son. May the bloodied crown stay lost and forgotten."

This is the first time the name "Menethil" was mentioned as a surname.