You can't have new and old logos to somehow show that something is new and something is old.
Well, you can do what you like but it's stupid.
You have a company and one identity. You only use one on your headed paper, website, social media etc so to continue using the old logo is just idiocy (IMO). It serves no purpose, other than to make you look incompetent.
You might say you won't change all the old logos straight away, to save money or for logistical reasons, but you can't then go and use the old logo on your brand new flagship fleet of trains. Nor argue that the contract was signed so there's nothing you can do.
If that was the case, as it's the DfT funding the livery and logos being put on, then you don't change the logo.
There was no good reason to change the logo anyway. The last logo was already new. It fits well with Great Northern, especially when GN and TL trains will work alongside each other on sections of track. It had familiarity, but was still independently recognisable. Useful for when you're at Cambridge and can see both on trains to London, but different onward destinations.
Nothing is going to convince me there was any benefit changing the logo, and it has just confused matters during the roll out of the 387s and 700s.