Using full number designations as names is unofficial. 1te, 2tes, 3te, etc. That's just a way of saying First, Second, or Third. Regiments were designated, by Prussian standards, as:
[Regiment Designation Number from Region][Region Name][Troop Type and Size][Regiment Name, if applicable][Regiment Number in the Army, if applicable] For Example (1815):
1. (1st Ostpreussisches) Grenadier-Regiment And, for the sake of the example... "Karl von Karlson", Nr. 1