Talk to some of the members of the Lyons' Pride in the Great Hall after gaining entry to the Citadel. They will tell you about a betting pool to try and guess Gallows' real name. You can ask Knight Captain Gallows about it after hearing about the bet. If your speech skill is high enough, you can convince Gallows to tell you his real name. After you find out his name you should speak to Paladin Glade, who is running the betting pool. Glade can be found near Gallows in the Great Hall in the A Ring area. Gallows tells you his real name is "Irving", and asks that he just be left alone.
Glade may die during the assault on Project Purity, if this happens the quest cannot be completed and you will not get the 1000 caps. Confirmed on all platforms.
Convincing Gallows to tell you his name is one of the most difficult speech checks in the game. Even with 100 Speech and 9 Charisma, you may not have a 100% chance of passing the speech check. With all expansion packs and latest updates added, the player needs 100 Speech and 10 Charisma to get the speech check success chance to 100%.
This unmarked quest can easily be done by simply waiting right before you tell Sarah Lyons of the Lyons Pride "I am ready" because all of the Lyons' Pride will be standing together making this quest an easy endeavor.
Sometimes Glade can be found in the B-Ring (the brig), particularly if it is late at night.
"Gallows humor" is a type of humor that arises from stressful, traumatic, or life-threatening situations; often in circumstances such that death is perceived as impending and unavoidable. It is similar to dark comedy but differs in that it is made by the person affected.
This side quest is another reference to the film Saving Private Ryan, which is centered around a squad of WWII soldiers led by Captain Miller (played by Tom Hanks). Some members of his squad have a betting pool to try and guess what Captain Miller's job was before the war, something he himself refuses to divulge.