Is there a specific meaning behind the TIE designation used in the names for the Galactic Empire's starfighters (TIE Bomber, TIE Fighter, and TIE Interceptor) and if so what is it?
TIE stands for Twin Ion Engine - sub-light propulsion technology behind these small fighter/bomber crafts.
TIE itself is not initially associated with the Empire, but the Empire commissioned these fighters on such a large scale that it made them their signature craft during the Galactic Civil War.
Out-of-universe, the name was coined by George Lucas, because they look like a bow tie.
Though the term "TIE Fighter" was coined because George Lucas thought they looked like bow ties, the ion engine is a real-life type of spacecraft propulsion, and publicity surrounding the launch of the SMART-1 spacecraft, particularly the shuttle Smart-1, likened its ion thruster to the propulsion systems of a TIE Fighter.
Twin Ion Engine
This is mentioned in various canon sources but the easiest one for me to reference from is Star Wars Encyclopedia of Starfighters and Other Vehicles. This includes the following pages where the TIE Striker and TIE Reaper have their models referred to as "Twin Ion Engine striker x1" and "Twin Ion Engine reaper".