No, none of the other children had Burgess in their name. George and Mary's other children were:
Mary, born 10 May 1794, christened 23 Jan 1795 in Stroud
James, c.11 Feb 1798, George in Stroud
George, born 7 Oct 1800, christened 2 Nov 1800 in Stroud
Henry, c. 8 May 1805 in Stroud
Richard, c.14 Jul 1805 in Stroud
Sarah Herson, c. 5 Jun 1807 in Cheltenham
Edward Jordan, c. 13 Aug 1809 in Cheltenham
Emma, born about 1816.
I am descended through their second son George, he was my 4xgreat-grandfather.
Mary died in 1851 in Kensington, but I haven't found George Senior's death yet, or christening either.
I'm hoping to get to the Gloucestershire RO sometime later this year, it's just a case of finding the time...
Megs