Side handle

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) They appeared in the place of humanoid ears. (PROSE: Doctor Who and the Revenge of the Cybermen)

Recognition
Upon discovering the Cybermen in Pete's World, Rose Tyler realised that she had seen the head of a Cyberman before, at Henry Van Statten's collection. (TV: The Age of Steel)

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

Variants
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 chest units. (TV: The Age of Steel)

The Mondasians' side handles were linked by a central energy weapon which was capable of killing humanoids, burning through steel, and damaging more advanced Cybermen. (TV: The Doctor Falls)

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)

A Cyber-Controller which used Borg technology sported an modified Cyber-helmet, the right side handle of which was replaced with a tube connected its faceplate's right eye, which was augmented with a Borg implant. (COMIC: Assimilation²)

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)

In Pete's World, EarPods worn by humans that had yet to be upgraded could be used by Cybus Industries to access their knowledge, such as in the case of Jackie Tyler. 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)

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)

The CyberKing's human control unit was converted using a side handle headset that connected the subject's mind to the CyberKing, changing their speech patterns and their eye colour throughout the process. Once the conversion was complete, the controlling unit could operate the CyberKing's movements and in the case of Mercy Hartigan could even take command of the Cybermen themselves. (TV: The Next Doctor)

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

Ashad, who was addressed as "Leader" by his Cyberguards, had mostly silver side handles with black corners, (TV: Ascension of the Cybermen) similar to the converted Alistair Gordon Lethbridge-Stewart. (TV: Death in Heaven)

In place of side handles, the Cyber-helmets of CyberMasters created by had large, silver Time Lord headdresses, with Gallifreyan symbols. (TV: The Timeless Children) Later, during the Master's Dalek Plan, the Cyber-Leader was distinguished by a silver headdress, its immediate subordinate's was coloured black whilst the other CyberMasters had conventional side handles. (TV: The Power of the Doctor)

Individual cases
By the time it was modified to serve as the Chess-playing Cyberman, a Cyber Legion shell was missing its left side handle. (TV: Nightmare in Silver) Similarly, UNIT's Black Archive contained a damaged, Cybusman-type Cyber-helmet which was missing its left side handle. (TV: The Day of the Doctor)

Behind the scenes

 * A Mondasian Cyberman appears briefly in the 2017 webcast Merry Christmas!, wearing fake reindeer antlers in place of its emotional inhibitor "side handles" and carrying a sign that reads CHRISTMAS WILL BE UPGRADED.