[Tim]

Here's the same overall code I posted in this thread but, with some modifications for you....

local function getPlayerColors(unit)

   if not UnitExists(unit) then return end

   local color
   local class = select(2, UnitClass(unit))

   if UnitIsPlayer(unit) then
      color = (CUSTOM_CLASS_COLORS or RAID_CLASS_COLORS)[class]
   else
      color = FACTION_BAR_COLORS[UnitReaction(unit, "player")]
   end

   return color.r, color.g, color.b

end

local UpdateColor = CreateFrame("Frame")
UpdateColor:RegisterEvent("PLAYER_ENTERING_WORLD")
UpdateColor:RegisterEvent("PLAYER_TARGET_CHANGED")
UpdateColor:RegisterEvent("PLAYER_FOCUS_CHANGED")
UpdateColor:RegisterEvent("UNIT_FACTION")
UpdateColor:SetScript("OnEvent", function(_, event)

   _G["PlayerFrameNameBackground"]:SetVertexColor(getPlayerColors("player"))
   _G["TargetFrameNameBackground"]:SetVertexColor(getPlayerColors("target"))
   _G["FocusFrameNameBackground"]:SetVertexColor(getPlayerColors("focus"))

end)

for _, BarTextures in pairs({TargetFrameNameBackground, FocusFrameNameBackground, PlayerFrameNameBackground}) do
   BarTextures:SetTexture("Interface\\TargetingFrame\\UI-StatusBar")
end

btw, PLAYER_FRAME_CHANGED will not work as it's not a valid event. -> https://wow.gamepedia.com/Events

I can't test this right now but, it should work.