What are the consequences for intentionally providing false information to an online site?

Question

Suppose you provide a false name and birthdate to a site like Facebook or some other online site that requires accurate information. You do not make any financial transactions or impersonate anyone (you use the name John Doe for example), and you are old enough to use the site in real life. Aside from permanently banning you from using their services (for violation of Terms of Service), can they legally do anything else? Are they likely to legally do anything else?

What if you were not old enough to use the site originally, but are now (say, you created an account at age 12, which is generally not old enough to use websites, but are now eligible)? What if your use of false information allows you to create multiple accounts in violation of the Terms of Service, but this does not lead to any damages? For example, suppose a social media site wants to prevent duplicate accounts, so it searches for users with the same name, birthdate, and IP address, but since you used your real name and birthdate on one and false information on the other, the social media site assumes these are different users.

Assume that this process never required making a fake ID.

Answer 1

There are three main aspects to this:

1. Its their website, and their terms of service. They can enforce those terms, or change them (in some appropriate manner). You have no recourse if they remove you, block you, or delete your account, for example. That's the measure that you would probably have, virtually every time.
2. To claim damages, or litigate beyond just website access control, requires a legal claim. But there's a catch there. To claim damages, they need to show actual damage, which they wish to be compensated for. If you misused their website but no actual harm can be shown, the total damage claimable is zero, whether or not you followed their rules. Merely entering dishonest information isn't by itself harm. So they would have to show they suffered damage/harm because of that, which is directly attributable to your behaviour, was foreseeably harmful etc, or similar. They also need to consider legal costs, and ability to enforce, especially if you are in a different country.
3. If for some reason the computer use was also illegal, then a criminal act could be committed and they could notify law enforcement. For example suppose you did this in the little known country of Honestania, where the law says that to prevent trolling and online abuse, anything posted on social media under any but your own legal name is a crime. Or suppose you'd been banned from the system and ignoring/evading such a ban was criminal computer use or criminal trespass due to the forbidden/unauthorised access (which can happen in several places). But this is purely for completeness; I guess you'd know if you were taking it further, into criminal computer use.