Well you can try this.
Code:
TargetFrame.nameBackground.show = TargetFrame.nameBackground.Show -- store the original Show.
-- background off
TargetFrame.nameBackground.Show = TargetFrame.nameBackground.Hide -- replace show with hide.
TargetFrame.nameBackground:Hide() -- hide it
-- (optional) background on
-- TargetFrame.nameBackground.Show = TargetFrame.nameBackground.show -- put the original Show back.
-- TargetFrame.nameBackground:Show() -- show it
This will make it so it doesn't re-appear when you switch or refresh target.
If you don't want the ability to restore it you don't need the first line or the last 2.