The bank robbers refer to each other as names from t.v. shows. Dr. Huxtable is from The Cosby Show, Dr. Howser is from Doogie Howser, MD, Dr. Quinn is from Dr. Quinn, Medicine Woman, and Trapper John is from M.A.S.H. (as mentioned in the show.)
Castle comments that the bank robber Dr. Howser could have picked a better name as an alias. Nathan Fillion was in Dr. Horrible's Sing-Along Blog (2008) with Neil Patrick Harris, the actor who played Doogie Howser.
While on the phone with Beckett before the bank robbery begins, Castle expresses his disdain for the paperwork side of being her partner. An amusing irony is that all it essentially requires of him is for him to write.
When Castle persuades "Dr. Howser" to let him go to the bathroom, he asks the gunman why that name when there's much cooler choices, specifically "Dr. House" ("House") and "Dr. Shepherd"("Grey's Anatomy"). Bryan Spicer, the episode's director, also boasts episodes of "House" on his resume.