Character
A character is a fictional depiction of a Transformer, a human, an alien or another entity that might or might not have a toy representation. If there is a toy, the character is usually, but not always, based on the toy and intended as a means of promoting said toy.
Over the course of the numerous Transformers series and toy lines, some characters have changed their names, while in other cases, characters have appeared that share a name with another character but are separate individuals. Many characters also have counterparts in other continuities they may or may not share a lot of similarities with.
Hasbro's attitude towards the importance of characters has changed a lot since the launch of the Transformers brand in 1984.
Character depiction
A character can be depicted in several ways. One of the simplest forms is the bio often featured on the back of a toy's packaging, which is usually a brief write-up of the character's personality and abilities.
Characters are also featured in supporting media such as comics, TV shows, movies, video games or books. In the case of characters based on a toy, the depiction of the character will often be consistent across the various media–in theory, at least.
Often, characters not based on existing toys may be created specifically for supporting media. They may be humans, but also Transformers or other aliens. In some cases, the same non-toy character appears in several different supporting media. Some of them might be turned into toys later on, due to the (often unexpected) popularity of those characters.
Relevance
Originally, Hasbro didn't put as much emphasis on outstanding characters for the Transformers toy line from a marketing standpoint as they do today. Toys were supposed to have a shelf life of two years at maximum, to be replaced by new toys, which would be entirely new characters. As a consequence, Hasbro only bothered to register a small number of trademarks in the 1980s, such as "Optimus Prime" or "Soundwave".
Hasbro didn't originally realize how much of a crucial part recognizable characters had played in the success of the original Transformers series until they were facing the viewer backlash following Optimus Prime's death in The Transformers: The Movie. Following that, more and more toys were designed to resemble–and named after–existing toys/characters. Starting with the Generation 2 toy line, Hasbro began basing many toys from nearly every new line on existing "classic" characters.
Same or different character?
Considering the large number of different Transformers toys, toy lines and continuities, there have been many instances where a character has used a dfferent name, two or more characters shared the same name, and a character has different incarnations in different continuities. Figuring out whether two characters are actually one and the same or not may sometimes be a difficult task even for longtime fans, and in some instances people's views on the matter may differ.
Same universe, same character, different name
Sometimes the same character might be known under different names. This can have multiple reasons: For example, Hasbro might want to release a reissue of an old toy, or a new toy based on an existing character, but the trademark for the old toy's name might no longer be available. As a consequence, they will chose a different name for the new toy, even though it's very obvious it's still intended to be the same character. For example, Bluestreak's modern toys are usually released under the new name "Silverstreak", Hot Rod's new toys first became "Rodimus Major" and later simply "Rodimus", and Bombshell has been recently renamed into "Hardshell" for the same reason.
Sometimes, a character changes his name in a very short span of time. A frequent reason for this is that Hasbro and Takara plan to release a new toy that represents an "upgraded" form of the original toy/character. To emphasize the change, the character and his toy get a new name. For example, Hot Rod was upgraded into Rodimus Prime in The Transformers: The Movie (1986), and Cybertron Overhaul later became Leobreaker.
Usually those name changes are reflected in the accompanying fiction, including the supporting media. Sometimes a name change is also exclusively used in fiction to explain the "origin" of a character: For example, the Generation 1 comics by Marvel UK revealed that the Dinobot Swoop used to go by the name "Divebomb" until a Predacon humiliated him and claimed the name as his own. Likewise, the Energon cartoon revealed that Wing Saber's original name was "Wing Dagger". Neither name was ever used for the corresponding toys.
Lastly, a character might also have different names for different markets. Takara usually calls their toys of Optimus Prime and Optimus Primal "Convoy", Jazz is better known as "Meister" in Japan, Sideswipe becomes "Lambor", and so on. In return, Hasbro gave many Robots in Disguise, Armada, Energon and Cybertron toys different names than their Japanese counterparts. Furthermore, some toys released in Europe after the original toy line had ended in the USA got different (but usually English or English-derived) names for different markets, and when Hasbro eventually released those toys in the USA as part of the Generation 2 toy line, they were renamed again. But since all name variants of those toys featured the same bios (albeit in different languages), they're commonly considered to be the same characters by fans.
It gets more difficult with unusual cases, though, particularly with toys and characters "imported" from Japan to the USA many years after the fact. Commemorative Series Ricochet is considered the same character as Headmasters Stepper; but is Masterforce Overlord and/or or the 1991 European release of the Overload toy, the same character as Heroes of Cybertron Gigatron? Are the Classics and Universe "Leo Prime" toys the same character as Beast Wars II Lio Convoy? Your mileage may vary.
Same universe, same name, different character
Sometimes two characters can go by the same name even though they're two entirely different individuals. The more common case is when two entirely different characters in two different continuities share the same name (discussed below); but this can also happen within the same continuity.
It started with Barrage the Insecticon from 1985 and Barrage the Micromaster from 1990, and Sky High the Pretender from 1988 and Sky High the Micromaster from 1990. Generation 2 introduced more same-name characters, as did Beast Wars and Beast Machines.
The Unicron Trilogy was equally guilty of this, with names such as Dirt Boss, Mirage and Downshift assigned to several different characters, most of them Mini-Cons. Hasbro did, however, attempt to avoid attributing the same name to two different Unicron Trilogy characters who weren't Mini-Cons. For example, an Energon character that resembles Generation 1 Wheeljack was named "Downshift", because the name Wheeljack had already been used by an Armada character.
Takara did similar steps to avoid attributing the same name to two different characters during their version of the "Micron Trilogy": For example, Armada Scavenger had been named "Devastar" in Japan, so Takara's version of Constructicon Maximus was named "Buildron" instead. And since the Micron Densetsu version of Armada Sureshock had already been named "Arcee", the Superlink version of Energon Arcee was named "Ariel" by Takara.
The Movie franchise once again gives us multiple characters within the same continuity using the same name, such as Movie Jolt and Revenge of the Fallen Jolt, or Movie Mudflap and Revenge of the Fallen Mudflap.
Once again, however, the line isn't always cut-and-dry: Are Armada Jolt and Cybertron Jolt the same or different characters? Is Movie Jolt, referred to as "Dead End" in the supporting fiction, the same character as Revenge of the Fallen Dead End? Are the two ROTF Dead End toys even the same character? Or, to use an example from above, is Masterforce Overlord the same character as the 1991 European release of the Overload toy? Once again, your mileage may vary.

