First-Name Basis/Web Comics

Megatokyo chapter 6, when Nanasawa Kimiko requests that Piro call her "Kimiko," followed by their least awkward conversation to date.
Parley in Gunnerkrigg Court switches from using her nickname for Andrew Smith (Smitty) to his first name after a Relationship Upgrade.
Wooden Rose Please, you must call me Aidan.
In El Goonish Shive, Adrian Raven asks Noah to refer to him as Adrian or Raven anywhere other than at school in this strip.
Off White: Iki with his adoptive mother. She's never really accepted her adopted son.
In Erstwhile, shortly before the wedding, the farmer's clever daughter call the king "sire," and he tells her that his name is Lennart.

Exceptions:

In Kevin and Kell, after Fenton officially gets engaged to Lindesfarne, he starts calling Kevin by his first name, at his suggestion.
In Close Encounters, a new transfer student allows the male protagonist to use her first name, which he finds shocking since they just met.
Squid Row We should be on a first-name basis.
Memoria Just Lucas, not Mr. Lucas.
Most General Protection Fault employees begin by calling Dwayne "Mr. Duncan" or "sir", but eventually switch to his first name.