Its source is an English expression meaning "Male child."
The name Sonny ranked 841st in popularity for males of all ages in a sample of 2000-2003 Social Security Administration statistics and 772nd in popularity for males of all ages in a sample of the 1990 US Census.
Though this name appears on the 1990 U.S. Census lists, it is used by only a small percentage of the general population.
This is a familiar nickname that any adult might use to address a young boy. Its use as an independent name, though still rare, probably owes something to singer-songwriter (and politician) Sonny Bono, who was born Salvatore Phillip Bono in 1935.