None of my Dragonborn characters take dragon names for themselves. However, their dragon enemies have given them names in the dovah tongue.
My blood-crazed red guard berserker, Shian, is known to them as Norok Sahqo Ven. The Fierce Red Wind. She runs untouched through the battle field and leaves crimson in her wake.
My breton mage, Kalin, is known among the dovah as Faal Lun Vahdin. The Leech Maiden. A vampire with a unslakable thirst for blood. Her gluttony is rivaled only by her guile.