To extend on what suchmoon said.
The way you prove that two Bitcointalk accounts are connected is if they use the same crypto addresses to receive payments (from bounties or signature campaigns), and if they use the same social media profiles. There are other ways, but this is one of them.

Imagine that you were banned on Bitcointalk with an old account. How do I prove that you are back with a new account? By looking at your wallet addresses and social media handles (if you have any, like suchmoon stated). If you are still using the same accounts to post on social media (as part of your bounty) as a person that was previously banned, there is enough proof to connect you to that banned individual.

But that is not all. I can use your information against you in an attempt to frame you.
I find a social media profile of someone who was banned from Bitcointalk. I sign up for a bounty with the information from that banned user together with some of your own info from a new account. You understand? After a few days, I report you to the admins for ban evading presenting the connection between you, the banned user, and the new account. If the admins don't care to check thoroughly and accept such "proof", you might get banned.

Do you see what just happened?
The ID of the Twitter profile of the banned user is KingLegend, for example (I just made it up). https://twitter.com/KingLegend/
Your Facebook ID is Kings.Den, for example. https://www.facebook.com/kings.den/
I create a Bitcointalk account and apply to a bounty using KingLegend as my Twitter account and Kings.Den as my Facebook account.

I have now managed to establish a fake connection between you, a banned user who used that Twitter account in the past, and a brand new Bitcointalk member who uses a combination of the two. What does that mean? It means that the new user is evading a ban, and you are an alt of that banner user because the two of you use the same social media profile.       

That's why I said that finding only a registration post with the same information as someone else is not proof of alt accounts. That new account will have to continue posting on social media as part of that bounty.