If the sign shape is perfectly symmetrical on the X axis except for the text, there is actually a better way to solve this instead of using a Mirror modifier and duplicating, rotating and merging the front to the back side if you want to keep it procedural rather than working destructively.
The "normal" Mirror modifier version:
Instead I would recommend to use the Array modifier and not mirroring the geometry. Place an empty at the roadsign's origin. Remove the Mirror modifier from the roadsign and add an Array modifier.
Disable the Relative Offset and enable the Object Offset, there you choose the empty as Object. Leave the Count at 2. I would also enable the Merge option (which I did not in the screenshot below).
At first it does not look like anything happened, you only see the (unmirrored) front and nothing at the back:
But when you select the empty now and rotate it 180° on the Z axis, you get a rotated duplicate of the front on the back, with the text oriented correctly and no need to apply a modifier and doing it destructively in Edit Mode.