Because at the time of acquisition, most of the free/paid users were die-hards, the competition for them was always AVG or Avast, and one who used either would not consider the other.
This also meant that doing an immediate shutdown of either AVG/Avast would mean a massive and sudden erosion of userbase, which would be very bad for two things: (i) Their cloud engine and (ii) The investors.
At the time of acquisition, AVG was a publicly traded firm with holdings from multiple firms, Avast was a private company. There were expectations to meet from the investors of AVG. To ensure that the investment into the purchase was worth the effort, the continued existence of the AVG brand was required.
Avast, as of 2019, estimates a good 3 years of value still to be generated by the AVG brand. That means, we're getting AVG branded products till 2021, complete with all developer references and driver names rebranded as AVG. Right now, AVG is an "independently developed product with Avast code". That will change, sometime in 2021/22 to "AVG by Avast" i.e. a rebranded product with all internal components Avast branded.
They may or may not keep the AVG brand running - as the aim for the company was to move Avast up the ladder to Enterprise/Business while AVG remains as a consumer oriented/free solution.
This was before the new Jumpshot controversy - now, with the revenue stream and bad press due to Jumpshot controversy, they may keep AVG running separately for longer (because AVG was less affected by this as the majority of articles were based on Avast).