What if Orwell had decided to name the ruling ideology of Oceania not Ingsoc but Newlab--short for New Labour? This would actually make sense on a number of different levels. "Newlab" would correspond to "Newspeak" for example. Orwell was of course a supporter (though sometimes critical) of the Labour Party, and he could make clear that this *new* Labour was something different from the traditional Labour Party he and other "oldthinkers" supported. In any event, it will make it a bit difficult for Tony Blair to talk about New Labour a few decades later...
From the title, I thought you meant like Orwell joined Labour instead of going into writing and rose to leadership. But let's go with this.
So why would he? Why would his publishers let him? English Socialism is a nice little generic term, and usable as a response to pro-Stalinism, something that Labour weren't during the post-war period, so why would be more specific? It'd ruin the mystic of the Party; "Oh, it's just Labour" (I apologize if that sounds mean, I'm writing on a phone. If I do come across as particularly aggressive, I'm not trying to be, and I do apologize if it comes out like that).
Also, Newlab sounds a bit like a New Newfoundland authoritarian state (Which I'm surprised has never come up on these forums). New Labour wouldn't enter the lexicon until 1994 when it came up as a confidence booster, so it's a bit out the time frame. But, if Orwell did use 'Newlab' and Blair tried to use it for Labour's re-branding, many an unfortunate comparison between Labour-Ingsog/Newlab would emerge. Could possibly cost Blair leadership.