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 1
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 recieving 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.
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 1 Megatron prior to the beginning of the series. (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 Leo Prime's Maximals on Gaia took modified names upon being upgraded by Angolmois energy.
Robots in Disguise
Megatron changed his name to Galvatron upon being upgraded.
Unicron Trilogy
Megatron has a tendency to change his name to Galvatron when he recieves a power boost. 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.