Howto register for an event with employer beside particpant
Part of the question is figuring out what you would like the end result to be.  What should the employer data look like in Civi?  The 'obvious' answer of an org record for the employer with an employer/employee relationship may not really be best.

There are many aspects to consider: If you have multiple registrations from the same employer, you don't want duplicate org records but do you want them all updating the same record?  Users may use different forms of the company name, or may use the same name to describe different parts/locations of the company.  De-dupe rules help avoid duplicates but you can end up with updates being applied blindly - ie the user does not know what data you already have and overwrites it.  On the other hand exposing your list of organisations and relevant data for them to select from has privacy concerns.

If you want to answer questions about who has attended your past events, then pulling in the employer from a relationship will give bad data if the participant has changed employer since the event.  You could try to look at the past relationships to find the applicable one at the time of the event but that gets awkward.

So... as often, there's no one answer that fits everyone.  One simple approach is to add custom fields for the employer on the participant registration profile.  If you really need a linked org record, you can create one manually.