Joe is the name of an ambulannce driver.
Behind the scenesEdit
As its mentions there was only one squad car when the ambulance made it to the crime scene, it must mean that either Mosely and the Uniformed Officer(Tony) was at the scene first, or the other two 'white' officers were there first. By the time Gabriel shows up there are two squad cars.
There is some confusing dialogue in the game, there is at least one individual presumably a police officer or the ambulance driver trying to find the way to the crime scene (but is lost in the fog). Molly (the female dispatcher) was definitely asking about Joe. The Coroner is mentioned in one of the dispatches that the 'Coroner requests assistance at' (which might actually imply that the Coroner was already at the scene).
It's more confusing in 20th Anniversary Edition as the line about Joe is mentioned by a man on the radio (and not necessarily the 'dispatcher', but it does seem "Molly" is male in that game). Oddly enough the ambulance is mentioned, but there is actually a Coroner van in the game instead.
In the novel for GK1 there are at least three characters named 'Joe' mentioned, see Joe (novels). One of which is the Coroner.
GK3 makes reference to the term 'average Joe'.