Charlus could refer back to the name Charles. It is derived from the Germanic karl or hari. It can mean "man" or "army,warrior". This can relate to many members of the Potter family.
Potter is a very common surname of English origin. It traditionally refers to the occupation of making pottery. Beatrix Potter was a well-known English children's author. Potter's field is the name for a burial ground for the unknown or unclaimed dead, particularly soldiers and orphans; the Potter family had many members that fit that description. The Potter Box is a model for making ethical decisions developed at Harvard University. J. K. Rowling has also commented that she has liked the name since childhood, as a family that had lived near her carried this surname.
However, J. K. Rowling has stated the wizarding Potter family's name was not of occupational origin; instead, it comes from the forebear of the family line, Linfred of Stinchcombe. Linfred's nickname, "the potterer", became altered to Potter over time.
There was some speculation that Charlus Potter was the father of James Potter and the paternal grandfather of Harry Potter. Later, Pottermore has revealed that Fleamont Potter, not Charlus, is Harry's grandfather. In spite of this, is still more than likely that Charlus was an uncle or cousin of James Potter and his descendants.
It is unlikely that Charlus comes from the same branch of Potters as Henry Potter -- Henry Potter's speaking out in the Wizengamot was why the family were cut off the Sacred Twenty-Eight as it was believed they were related to Muggles; if Charlus came from the same branch, he would be considered a blood traitor and Dorea would have been disowned.