Mashiach L. Bjorklund
There are a number of reasons why a person would travel under an older siblings name, here's a few:
1. Military conscription - the eldest son could sometimes be exempted for economic reasons from conscription. This would allow them to travel (or buy a ship's ticket to travel) where as a younger sibling who was facing or soon to face conscription would not be allowed to travel.
2. The ship's ticket was purchased under another name - once a ticket was purchased it could not be transferred to another person. But that did not prevent another person from assuming the ticket holders identity and using their ticket.
3. Age restrictions - This varied widely, but if a person was too young to travel unaccompanied they might have used an older siblings identity to purchase a ticket. Especially if there was no one at their destination to receive them upon their arrival. In 1912, a person 14 years or younger would have been considered a minor and could not travel without a designated guardian to accompany them. If the family had the economic means, they could hire a guardian (like a nanny), but if they lacked financial resources the minor would not be allowed to travel, or even purchase a ticket to travel. Keep in mind laws were not the only restriction. Steamship companies had their own rules as they were financially responsible for returning an immigrant if they were rejected at their port of entry.
Documents? That depends upon their country of origin, countries they traveled through, and ports enroute, etc. In very general terms, there was the ticket (which was also their receipt for purchase), that stayed with the person. There was something often referred to as a docket. That came from the steamship's ticket office and was used to add the person to the ship's manifest. This was not a legal requirement but used internally by the steamship line for passenger management. Most of those were disposed of after the ship sailed. Next up was the passenger manifest, created for the ship and matched to the passengers boarding, those were collected at the port of entry upon arrival. Next is the passenger arrival records, available through the National Archives and online via Ancestry and other genealogical database companies.
Keep in mind this is the simplest version of what's available. There are literately hundreds of books are written on this subject. Also go to familysearch.org. They have some good tutorials on the subject. There are even some good YouTube videos out there as well.