Side handle

The Mondasian's side handles functioned as the emotional inhibitor. (TV: World Enough and Time)

Side handles were the distinctive pair of handles which were located atop the Cyber-helmets of most Cybermen. (PROSE: Doctor Who and the Tenth Planet, TV: The Age of Steel, The Time of the Doctor)

Recognition

Upon discovering the Cybermen in Pete's World, Rose Tyler realised that she had seen the head of a Cyberman before, recalling the distinctive handle shapes. (TV: The Age of Steel)

The Eleventh Doctor gave the name Handles to his Cyber-helmet companion. (TV: The Time of the Doctor)

Variants

Cyber-Controllers were typically distinguished by their enlarged craniums which lacked side handles. (TV: Attack of the Cybermen)

Cyber-Leaders were distinguished by their black side handles. (TV: The Pandorica Opens)

In the case of the Mondasian Cybermen, the handles were a attachable headset which functioned as an emotional inhibitor, which was lacked by the first Mondasian patients. (TV: World Enough and Time) Conversely, the emotional inhibitors of the Cybermen from Pete's World were located within their chests. (TV: The Age of Steel)

In Pete's World, EarPods worn by humans that had yet to be upgraded could be used by Cybus Industries to access their knowledge. During this process, in which the oblivious subject was incapacitated, similar handles would form and connect from the two EarPods. (TV: Rise of the Cybermen)

Cyber-Controllers, such as the one who resided on Telos, were generally distinguished from their subordinates in that their helmets sported an enlarged cranium which forgone the handles. (TV: The Tomb of the Cybermen, Attack of the Cybermen) Conversely, John Lumic, the Cyber-Controller of Pete's World, had a Cyber-helmet with handles. He was distinguished by his brain which was visible behind the forehead's casing, and a set of four blue lights in each eye. (TV: The Age of Steel)

In both N-Space and Pete's World, Cyber-Leaders were typically distinguished by their black handle bars. (TV: Earthshock, Army of Ghosts) The leader of the CyberNomads had a black helmet with only a silver faceplate. (TV: Revenge of the Cybermen)

Cybershades had bronze Cyber-heads. Like their Cyberman superiors, they had piping like handlebars connected to their heads, except they angled diagonally like the ears of an animal. (TV: The Next Doctor)

Cyber-converted Raxacoricofallpatorians sported bulbous Cyber-helmets which matched the Raxacoricofallapatorians heads. Similarily, converted Judoon had rhinoceros-like Judoon horns atop their helmets. Converted Klingons were distinguished by helmets which matched the unique shape of the Klingon head, with extensions reminiscent of hair. (COMIC: Assimilation²)