We first heard about the name change for Microsoft's Project Spartan during the Day 1 Build 2015 Keynote in late April.
Since then Windows Insiders have checked every new public build of Windows 10 to see if the new Microsoft Edge name had replaced Project Spartan.
In the three Windows 10 PC builds since late April not one of them has ushered in this expected change from Spartan to Edge.
It now appears that this significant milestone in the development of Windows 10 is on the horizon as our Ring Master, Gabe Aul, has indicated they now have that branding on internal builds.
@Sparker0i Microsoft Edge branding is now in internal builds, will make it to you after next build.— Gabriel Aul (@GabeAul) June 9, 2015
From this tweet we can extrapolate that there are likely two more Windows 10 builds coming to Insiders before RTM which is expected sometime in July prior to the 29 July availability date.
The first build will still retain the Project Spartan branding on Microsoft's new browser while the second one will see the first public appearance of this browser as Microsoft Edge.
I would also expect further fit and finish to the browser as we are seeing in other areas of the OS as the final weeks of development continue.