I'm betting that his legal name on his credit cards and license and birth certificate are all Homero... so... yes... He would use Homero in legal proceeding... Since that is his real actual given first name...
Yes, but you can sign up for Amazon with any name you want, especially the Amazon account name. On this basis, I would surmise Homero would just use 'Josh' most of his online accounts do.
Whatever, just seems silly all in all.