No. "Stonewall" Jackson was Thomas Jonathan Jackson-- Stonewall was a nickname he gained while a Confederate general in the Civil War. President Andrew Jackson was born in 1767 and died in 1845. General Stonewall Jackson was born in 1824 and died during the war in 1863, ironically as a result of "friendly fire."
"Stonewall" Jackson's given name was Thomas Jonathan Jackson -- "Stonewall" was a nickname he received during the Civil War as a Major general in the Confederate army. No modern celebrity named Jackson is directly descended from Stonewall Jackson, as his only surviving child was a daughter born in 1862.