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)

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)

Uniquely, Cybermen whom participated in an alternate Last Great Time War had helmets whose side handles pointed down rather than upwards. (COMIC: Prologue: The War Doctor)