This is a gift from Ulysses upon besting him and the Divide and making it out in one piece, the exact style you receive depends on your actions in this area. If the courier sides with the New California Republic, the emblem is the two-headed bear; if he sides with the Legion, the symbol is the bull; if he sides with Yes Man, the emblem is a black spade with the number "21" imposed over it. However, if they side with Mr. House, the emblem will be the same Old World flag as on Ulysses' duster.
At the entrance of Canyon wreckage, in the footlocker after completing Lonesome Road.
Despite the four variations, they all share the same ending slide: the Courier walking off into the sunset while wearing the independent (Yes Man) variant.
The spawn script is apparently based on overall raw reputation "points" rather than the shown reputation threshold, and is not affected by the actual quest line the player is following.
Wearing a faction-specific armor before confronting Ulysses can change which duster you will receive. For example, if you are favored with the NCR, but wear an NCR disguise, your fame with them will be set to neutral and your second-highest fame will become your highest for the duration you wear the disguise.
The NCR version is the only piece of equipment that directly increases the Courier's maximum carrying capacity.
The "Old World Justice" version is an exact copy of Ulysses' duster cosmetically, though they give different skill boosts.
This is the only armor in the game that changes based on your reputation points.