Decided to do it a few hours early...
:
On eSato, randomuser, Detox and maiaramdan confirmed the existence of three H2 or Q3/4 2013 Sony phones:
Sony C670X ('Honami') - although the C670X could possibly be called the
'Togari' (see below),
Sony C680X ('Gaga') - although this will quite likely be called the
Sony Xperia 'ONE' (see below) , and the
Sony C550x ('Dogo'):
randomuser explicitly confirmed the Sony C670X and the Sony C680X, when he said "Guys, no discussion on these please

I can reveal one though. C670X = phablet.

"
"Woah. Just 2 days back I revealed the C680X model number and its already leaked :-o"
"Ummmmm. C680X is not Phablet."
Later on in the thread randomuser confirms the other two:
He explicitly confirmed the Sony 'Dogo' when he said "Dogo should leak soon

".
He confirmed the Sony 'Gaga' acidentally when he replied to someone who had identified that it had been leaked from eSato to phonearena when his reply said "It was no member, but PA spies who picked it up. "
Detox confirmed some others: "Xperia Tablet Z = Pollux = C690x
Xperia ? = Gaga = C680x
Xperia ? = Honami = C670x
Xperia Z = Yuga = C660x
Xperia ZL = Odin = C650x
Xperia ? = Dogo = C550x
Xperia SP = HuaShan = C530x
Xperia ? = Togari = C360x
Xperia L = ? = C210x
Xperia E Dual = Nanhu_DS = C160x
Xperia E = Nanhu_SS = C150x
Am I doing this right?"
There will also be a Sony C680X leak in April, as confirmed by Ambivalent "We will reveal that information in April. Please do not ask about C680X until than." in reply to the following question "So lets see whether Sony C680X use snapdragon 800 or 600(mostly will be this one) or still APQ8064?"
maiaramdan and randomuser accidentally leak the Sony Xperia 'ONE': "...wait till you see C680x aka SONY - ONE" "wait and see
we decide not to talking about SONY - XPERIA ONE now" "No discussing the C680X please."
There was also some very good speculation from some users:
coolkid8689 speculated that: "My guess is,
C670X = Phablet without water-proof...
C680X = Phablet with water-proof... Now give me nobel prize please...

" which would be in-line with Xperia 5/5R rumours from December 2012, with the 5R being the dust/waterproof variant of the Xperia 5.
stedus speculated that: "So C670X will be Togari and C680X will be Gaga?

" (to which Ambivalent quickly replied: "Cannot confirm anything I already posted too much stuff. Please refrain from asking about 2H phone.")
Sources:
http://www.esato.com/board/viewtopic.php?topic=204753&start=4335 ,
http://www.esato.com/board/viewtopic.php?topic=204753&start=4380 ,
http://www.esato.com/board/viewtopic.php?topic=204753&start=4410 ,
http://www.esato.com/board/viewtopic.php?topic=204753&start=4485 ,
http://www.esato.com/board/viewtopic.php?topic=204753&start=4545 ,
http://www.phonearena.com/news/Sony...be-the-rumored-5-Gaga-flagship-for-H2_id39835