Admin > User Accounts > Manage Profile Properties > Add New Profile Property.  This allows you to create a custom profile property for each user.  Once you created it you can then manage it just like out of the box profile properties.  The user then updates it at registration and profile manintenance.  It sounds like you need to use the List data type, with one entry for each Company.  (Oddly the lists you can create via the host account are out of bounds so you can't use any existing list). 

The bad news is that lists don;t seem to quite work in 4.5.5.  I'm using the functionality to give each user the option to define what sort of e-mails they would like to receive.  However, I can't get the custom profile property to work quite right.  Yes /No fields are OK but lists are a just ignored -  a blank drop-down box appears with the list values ignored and no input is possible. 

you can force the profile page to be displayed beneath the registration form by setting the option "user profile required before registration" in "user settings".