The link given above is the best resource available. Depending on time period and citizen class of your character, the name would be different.
The only people to call someone by their praenomen: Marcus, Lucius, Gaius, etc. would be immediate family and really close friends, assuming your character is upper class. If your character is a middle-class citizen, foreign-born citizen, or freed slave, then this changes.
If you want your upper class character to be called Turibius by most in the story, then you'll want Turibius to be the characters nomen. So, he could be Gnaeus Turibius Drusus... though, Drusus, depending on your time frame is a very dangerous name in Rome during the time of the Empire. Dangerous enough to have the need to hide your name to be spared from the death trials.
Caelius is pretty safe, though, for a name.
My suggestion, not knowing any of your story's details, is this: pick one of the common praenomen off the link, then add Turibius Caelius to the end. Have anyone outside of family call him by Turibius Caelius and his family call him the praenomen.
All of this advice comes from a high school Latin teacher in the know. Use at your own risk.