What's in a name? A Wheeljack by any other name would cause as many explosions.
For a Transformer, a name is not just a convenient handle for referring to someone--it's a way to describe yourself. As a result, Transformers sometimes take new names upon going through major changes.
Generation One[]
Jazz's real name is unpronounceable in English, so just call him Jazz. Man of Iron! This may imply that the Transformer names as we know them are generally English aliases.
Probably the most famous name changes are the new names taken by the faction leaders. Different versions of Optimus Prime have had the previous names Orion Pax and Optronix, Megatron changed his name when he became Galvatron, and Hot Rod (alternatively known as Rodimus Major or just Rodimus) became Rodimus Prime upon receiving the Matrix. In addition, Bumblebee has displayed a tendency to change his name to Goldbug.
Other Transformers have changed their names in specific universes; for instance, the most prominent version of Elita One was once known as Ariel, and one version of Outback changed his name to Fallback. Also, Swoop was called Divebomb in the past in Marvel Comics continuity and Dreamwave comics continuity.
Beast Era[]
Nearly every member of the Axalon and Darkside crews appeared to take a new name upon first taking an animal alternate mode. Similarly, Megatron renamed himself after Generation One Megatron prior to the beginning of the series, so it is unclear what his real name was. (Although Airazor and Tigatron were active prior to the Beast Wars, it is not clear what names they used previously.)
Several of the Predacons who fought Lio Convoy's Maximals on Gaea took modified names upon being upgraded by Angolmois energy. While Lio Convoy was just called "Convoy" before scanning.
In Beast Wars II, a rookie Convoy changed his name to "Lio Convoy" after scanning a mysterious white lion.
In Beast Wars Neo manga, Big Convoy was originally named "Big" before becoming a Transformer.
Robots in Disguise[]
Megatron changed his name to Galvatron upon being upgraded, while the Autobot Brothers simply added the prefix "Super" to their names.
Unicron Trilogy[]
Megatron has a tendency to change his name to Galvatron when he receives a power boost and a color change. Others, such as Overhaul and Cyclonus, prefer to reserve name changes for when they are upgraded into entirely new bodies.
In the Japanese version of the Unicron Trilogy, characters change names whenever they get a new body.
Transformers Animated[]
Following the same rule in Beast Wars when Elita-1 and Wasp acquired beast modes, they changed their names to Blackarachnia and Waspinator respectively.