I don't know if companies hire artists to specifically design/model characters, but it's ringing some bells, so I wouldn't be surprised if they do. This link
is to the art section of www.gamasutra.com's
job board. I suggest you scan the list for a job description that fits.
Here's one that might be what you're looking for:
The point of this is for you to gain some information on the types of art/character modeling jobs there are, and maybe figure out what kind of skill set you need to get a job. But beware: this industry is very competitive...