So I lied. Grey's Anatomy did have a naming event though it happened in the past. (Thanks, Alaina!) It's from a developing story line that began with the ferryboat arc* when a pregnant Jane Doe had her face squished beyond all recognition and amnesia to boot. Alex, the lecherous leech, manages to care for this Jane Doe even going so far as to name her Ava and basically falls in love with her the best he knows how. Well Ava remembers that she's Rebecca and her husband comes back to get her. Later on Rebecca comes back looking for Alex, they make a trip to the on call room, and just a couple episodes ago she comes back again saying she's pregnant. Izzie runs some tests and finds out she's not. Rebecca tries to get breast implants because she wants her body to match her face. Things are very very weird. And then Izzie tells both Rebecca and Alex that Rebecca's not pregnant and Rebecca snaps, barely functioning, practically catatonic snappage. Alex takes care of her in very sweet unlecherous ways, but it doesn't end well. Rebecca tries to slit her wrists, Izzie has to hospitalize her against Alex's wishes and in the midst of arguing totally fumbles over Jane Doe's name. Is she Ava? Is she Rebecca? We don't know. We find out she's been diagnosed with a borderline personality disorder that was pushed over the edge by all the ferryboat drama.
So that's the background (with lots of spoilers, sorry!). What's with all this naming? Well first Jane Doe as Jane Doe wasn't going to survive. Alex's naming grounded her and really was integral for her recovery. Even after she got back her memory, she clung to the identity she had as Ava. Ava and Rebecca were not the same person. They had different lives, different loves. When Izzie is running tests on Rebecca, Rebecca says she wants to start over and have a baby in a way that she had already had her baby in this hospital. She's totally dissociated herself from her husband and child.
I've always been fascinated by personality theory and identity development. According to Erik Erikson, identity formation is integral to moving on from identity vs. role confusion to intimacy vs. isolation. Because Ava's identity was tied up with her intimacy with Alex, she was codependent. It would have happened to anyone who wasn't borderline neurotic. In fact, I don't think they even needed that plot twist. You can just do the same thing with names.
*AKA when Grey's Anatomy tried to jump the shark. Sorry I'm still bitter about the end of Season 3, loyal, but bitter).