If you click on the bold lettering above, it should take you to a list of names, but I did not find Joseph Twist or Mary Brown in the record, so I assume that they were buried at some other location. There were a lot of Mary Browns. Here are some with parents named.
Mary Brown
England Births and Christenings, 1538-1975
birth: Killis Lane
christening: 28 September 1796 Horsley, Derbyshire, England
residence: Horsley, Derbyshire, England
father: Exuperius Brown
mother: Eliz. Brown
Mary Fenlison Brown
England Births and Christenings, 1538-1975
christening: 18 April 1797 Liverpool, Lancashire, England
residence: Liverpool, Lancashire, England
father: George Brown
mother: Diana Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 7 May 1797 Prestwich, Lancashire, England
residence: Prestwich, Lancashire, England
father: Benjamin Brown
mother: Esther Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 4 June 1797 Prestwich, Lancashire, England
father: Joseph Brown
mother: Isabella Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 4 June 1797 Prestwich, Lancashire, England
residence: Prestwich, Lancashire, England
father: Joseph Brown
mother: Isabella Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 24 December 1797 Prestwich, Lancashire, England
residence: Prestwich, Lancashire, England
father: Matthew Brown
mother: Mary Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 15 October 1797 Leigh, Lancashire, England
residence: Leigh, Lancashire, England
father: John Brown
mother: Alice Brown
Mary Fonlison Brown
England Births and Christenings, 1538-1975
christening: 18 June 1797 ST NICHOLAS, LIVERPOOL, LANCASHIRE, ENGLAND
father: George Brown
mother: Diana Brown
Mary Brown
England Births and Christenings, 1538-1975
christening: 24 December 1797 Prestwich, Lancashire, England
father: Matthew Brown
mother: Mary Brown
Mary Brown
England and Wales Non-Conformist Record Indexes (RG4-8), 1588-1977
christening: 8 June 1797 Liverpool, Lancashire
father: William Brown
mother: Ann Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 5 October 1817 Manchester, Openshaw, Lancashire, England
father: Thomas Brown
mother: Mary Brown
Mary Ann Brown
England Deaths and Burials, 1538-1991
burial: 2 February 1845 Manchester, Lancashire, England
father: William Brown
mother: Mary Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 16 March 1846 Manchester, Lancashire, England
father: John Brown
mother: Ann Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 25 March 1827 Middleton (Near Manchester), Lancashire, England
father: Robert Brown
mother: Mary Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 10 January 1818 Middleton, Lancashire, England
father: George Brown
mother: Jane Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 6 May 1806 Hrist Church, Salford (Near Manchester), Lancashire, England
father: Thomas Brown
mother: Alice Brown
Mary
England Deaths and Burials, 1538-1991
burial: 19 November 1813 Chapel Of Upholland, Wigan, Lancaster, England
father: Henry Brown
mother: Jane Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 17 December 1806 Ardwick, Lancashire, England
father: Jonas Brown
mother: Ann Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 9 October 1809 Openshaw, Lancashire, England
father: Francis Brown
mother: Ellen Brown
Mary Brown
England Deaths and Burials, 1538-1991
burial: 5 May 1832 Manchester Collegiate Church, Lancashire, England
father: Thomas Brown
mother: Elizabeth Brown