so i made a copy of my certificate of citzenship

Now. suppose my name was Harris John Doe (harris being a family name, siblings have same first name) as written on my birth certificate...
But my school records since kindergarten say John Harris Doe, my DL says John Harris Doe, my social security says John Harris Doe, but legally (birth certificate and citizenship) i am Harris John Doe... will i have problem with getting my CHL?
i mean my school, DPS for driving, or social security never cared.