This is always repeated on reddit but it is not true. The names are chosen by a computer program, it is supposed to be random based on NFLPA rules.

Each week during the preseason and regular season, ten (10) Players on every Club will be tested. By means of a computer program, the Independent Administrator will randomly select the Players to be tested from the Club’s active roster, practice squad list, and reserve list who are not otherwise subject to ongoing reasonable cause testing for performance-enhancing substances. The number of Players selected for testing on a particular day will be determined in advance on a uniform basis. Players will be required to provide a specimen whenever they are selected, without regard to the number of times they have previously been tested consistent with the limits set forth in the Policy