I can understand why "Greater Anglia" was chosen as it covers both West Anglia & East Anglia parts, both previously served by separate TOCs, bringing the two together under one umbrella. They could have chosen "Anglia Trains" or "Anglia Railways" (like the defunct TOC).
I was intrigued by reading from elsewhere by the fact "Greater Anglia" wasn't chosen by Abellio however by the DfT.
As the DfT had a "thing" for traditional names, why "Great Eastern Railway" wasn't chosen I don't know. I presume this was before Grayling's tenure and now he is no longer the Sec, and it is looking likely that West Coast would be branded as "Avanti" instead of "LMSR".
The renaming of SWT to SWR, LM to LNR, EMT to EMR and VTEC to LNER all happened under Grayling's watch.
Then the "Greater Anglia" name could still continue, even if it changes hands from Abellio to whoever in the future, instead of "Great Eastern Railway" or "Great Anglian Railway".