This character is infamous, someone who is known for a reputation that's not exactly regarded positively in public eyes.
The counterpart of being famous, this character is well known for some bad quality or deed. Note that being infamous does not mean one is automatically a criminal or villain or evil, many infamy can be created due to the character's reputation, wide spread rumors, and/or the person being misunderstood, the same as how positive fame is spread, only towards a more negative note.
ex. being a lone wolf that is well known for some reputation yet most people hesitate to interact with him/her due to said reputation and/or maybe along with their intimidating air, but in fact that person may have a heart of gold or is just misunderstood.
On the other hand, it's also possible for one person to be both famous and infamous at the same time, being well known and revered to positively on one hand in one group, while at the same time resented or feared by some other group of people or even seen as an outcast with a formidable and/or notorious reputation.
On another note, many criminals and villains usually have a reputation of infamy. However, it should be noted that although criminals, villains, and generally evil characters are usually infamous, infamy does not automatically mark someone as evil as explained above. Many anti-heroes can have a degree of infamy, the same as how a villain can actually be famous positively but it's actually a mask to hide their true selves and goals as well as using the public to their advantage.