[Xrystal]

Off the top of my head I can only think of tracking down which function is the last point of updating the name fields of any Unit Frame and hook into it so that you can replace the name with your alternative... but some that I found returned straight out so not sure if they would follow on with your custom code.

For example:
https://www.townlong-yak.com/framexm.../UnitFrame.lua

Includes this function:

function UnitFrame_Update (self, isParty)
    if (self.name) then
        local name;
        if ( self.overrideName ) then
            name = self.overrideName;
        else
            name = self.unit;
        end
        if (isParty) then
            self.name:SetText(GetUnitName(name, true));
        else
            self.name:SetText(GetUnitName(name));
        end
    end
    UnitFramePortrait_Update(self);
    UnitFrameHealthBar_Update(self.healthbar, self.unit);
    UnitFrameManaBar_Update(self.manabar, self.unit);
    UnitFrame_UpdateThreatIndicator(self.threatIndicator, self.threatNumericIndicator);
    UnitFrameHealPredictionBars_UpdateMax(self);
    UnitFrameHealPredictionBars_Update(self);
    UnitFrameManaCostPredictionBars_Update(self);
end

It might be as simple as hooking into this function and just adding your random name and setting the text again. If not, it gives you a starting point to investigate.