Hi. I have a copy of "History of Edgar County" which states: The county was named for John Edgar, who was an officer in the British Army in 1775. He married an American wife, resigned his commission, and cast his fortunes with the colonists in their determination and effort to be an independent nation. Because of his military antecedents, his wife, who was a rich resident of Philadelphia, disposed of her estate and they came to the far western frontier. They located at Kaskaskia and, by virtue of their wealth and high character, became leading citizens in every way. . . . The special manner in which the county came to be named for General Edgar is only a matter of tradition. It is told that, when the General Assembly passed the act creating this county, Mrs. Edgar was at the capital and was given permission to name it, and she bestowed upon it her own name, saying, 'My husband gave this name to me; it is mine, and I give it to this new county -- I name it Edgar.'"
There is no biography of the Edgars in the Edgar County history but you might find something in the Kaskaskia area. Hope this helps.