John W. VanValkenburg had a brother George W, who was married to Sarah Ann Burgess. That may be where the Burgess names fit in.
Regarding the individuals buried in the Albany Rural Cemetery plot. #1 - Rufus Palmer was John Van Valkenburg's second wife (Louisa Allen Smith #15) first husband. He was born in 1833 in Austerlitz, NY near Chatham, NY. #2Mary R. Van Valkenburg would be Mary Rice, wife of John Van Valkenburg (parents Silas Taft Rice and Mary) #3 Anna L. Lyon would be Anna Louise Van Valkenburg, daughter of John W. VV and Mary Rice.She married Franklin Lyon. She was born 10/13/1850. They had a son, DeWitt Clinton (#14) who went by his mother's name VanValkenburg and not Lyon. Dewitt Clinton (Lyon) Van Valkenburg ws born 1/9/1872. He died 12/13/1907. Jennie Van Valkenburg was the first wife of DeWitt Clinton Van Valkenburg(above). They had a son DeWitt C Van Valkenburg who died as an infant. Dewitt Clinton's second wife was Mary Kelly. DeWitt Clinton (Lyon) Van Valkenburg lived much of his grown life in Brooklyn, Kings Co.,NY