[SDPhantom]

Looks like nameplates on classic behave differently than on modern.
Here's a more complete example with the changes.

--  Nametag font size
local function SetFont(obj,optSize)
    local fontName=obj:GetFont();
    obj:SetFont(fontName,optSize,"THINOUTLINE");
end
 
SetFont(SystemFont_LargeNamePlate,8);
SetFont(SystemFont_NamePlate,8);
SetFont(SystemFont_LargeNamePlateFixed,8);
SetFont(SystemFont_NamePlateFixed,8);
 
--  Disable nametag colors
DefaultCompactNamePlateFriendlyFrameOptions.colorNameBySelection=false;
DefaultCompactNamePlateEnemyFrameOptions.colorNameBySelection=false;
DefaultCompactNamePlatePlayerFrameOptions.colorNameBySelection=false;
 
--  Move nametag
hooksecurefunc(NamePlateDriverFrame,"OnNamePlateCreated",function(_,base)--   Hook nameplate creation function
    local unitframe=base.UnitFrame;--   UnitFrame attached to nameplate base
    unitframe.name:ClearAllPoints();--  Clear nametag anchors
 
--  Set new anchor(s) here
    unitframe.name:SetPoint("BOTTOM",unitframe.healthBar,"TOP",0,4);
end);
 
--  Remove realm names
hooksecurefunc("CompactUnitFrame_UpdateName",function(frame)
    if ShouldShowName(frame) then
        frame.name:SetVertexColor(1,1,1);-- Fixes tapped mobs permanently setting the nametag gray
        frame.name:SetText(GetUnitName(frame.unit));
    end
end);

Note: A recreation of the existing anchor is given to illustrate how to set an anchor from Lua. If you need more detail on the function, see fontstring:SetPoint().