Should I ask the user for their company name or email address as an additional source of validation?

During the signup flow of our service, we ask the user for their phone number and primary email address. We don't show those in their user profile. User can call each other only after they have matched.

We are now considering the possibility of showing the company the user work for in their profile. For that, the user would have to either:

  • Select their company from a list (can have an auto-complete text field for fast search); or
  • Enter their email address (and then we do the work of linking the domain name to the company)

Asking for the company name is:

  • (-) Harder to implement on the client apps (listing + autocomplete + keeping the company db up-to-date)
  • (-) Harder to later add some kind of verification to make sure the user actually work for that company (not a problem/requirement right now)
  • (+) Less privacy invasive: the user doesn't share his email address with us
  • (+) Better UX: Faster to enter/search for the company name than to type full email address

Do you see any other trade-offs? How would you go about asking for the company name and/or email address?