Initiate Reddin is an overly curious and excitable recruit on her first combat assignment. Vargas does what he can to restrain her and teach her the ways of the Brotherhood. Reddin was added to Sarah's unit against his advice (and probably hers), but although Vargas may act angry and annoyed at Reddin, it is entirely because he is trying to keep her alive.
Following in His Footsteps: Reddin gallantly fights alongside you in your journey to the Galaxy News Radio building in your pursuit for more information on the whereabouts of your father. During the quest, the explosion of the barrier of vehicles that heralds the arrival of the super mutant behemoth kills her instantly. After the behemoth battle, Sarah Lyons tells Vargas that she will tell the Brotherhood of Reddin's courage, and that she will now be known as Paladin Reddin.
If you proceed to Rivet City and speak to Doctor Li without going to GNR first, and then later go to GNR, you won't encounter the Lyon's Pride, Initiate Reddin, or either of the two dead Brotherhood of Steel initiates, and play through the encounter by yourself. The Lyon's Pride will then introduce themselves at the Citadel, minus Reddin.
Citadel information terminals and Citadel pesonnel terminals state her funeral has been put on hold due to unexpected tactical developments and that a memorial service will be scheduled, however the date is still to be determined.
In the terminal entry about her funeral, she is referred to as 'Initiate Reddin' rather than paladin.