Here are the possible solutions for doctor's insignia clue
Answer
Clue
Relevancy
caduceus
Clue
Doctor's insignia
Definition
(Latin) a Greek or Roman herald's wand; specifically the wand carried by the messenger-god Hermes or Mercury, usually represented with two serpents twined round it
badcase
Clue
Robert Palmer "___ of Loving You (Doctor, Doctor)"
fez
Clue
Shriner-style hat favored by Matt Smith's "Doctor Who" character, the Doctor
Definition
a red brimless cap of wool or felt
jodie
Clue
___ Whittaker, player of the first female Doctor on "Doctor Who"