Wikipedia says that the consuls were initially the king's counsels judging from the name of the office. I wonder whether it is the fact and is there any reliable evidence for consuls under reges?
It isn't that likely that the consul's name was taken from a kingly adviser, since in the initial years of the Roman Republic the name of the office was "praetor". Only later was the job renamed and praetor used for the judicial officers of the Republic.
A more likely derivation of the name consul is from con- and sal- "get together" because the two officers were supposed to come up with a policy together.