register for (something)
1. To enter one's name and details into an official list in order to do, receive, or participate in something. Be sure to register for a chance to win a brand-new 4K television. The class is filling up, so you'll need to register for it soon if you want to attend.
2. To enter someone's or one's own name and details into an official list in order to do, receive, or participate in something. In this usage, a noun or pronoun is used between "register" and "for." My case worker is registering me for an online class to improve my computer skills. I'm going to register my Pomeranian for a dog show next year. You should register yourself for the government's self-employed tax-break scheme.
register someone for something
to sign someone up to participate in something. Would you please register me for the workshop when you sign up? Excuse me. I have to go register myself for the contest.
register for something
to sign up to participate in something. Have you registered for the class yet? She is registered for the same classes as I am.