CA – Noncommercial Class A License & Registration

So, per Commufornia’s state law, I need a noncommercial class A to tow my new-to-me weekend warrior bumper pull toy hauler. Great.

Not that big of a deal I guess, just an inconvenience.

Does anyone know if I am going to have issues registering the trailer without the class A license? I bought the trailer used and would like to get it in my name.