Clergy at the Parish Churches
London, as with all of England, was divided up into geographical areas called parishes. Everyone who lived within the boundary of a particular parish was required by law to attend services at the church within that parish’s boundary. Parishes often took the name of their parish churches.
For people who lived within Paul’s Churchyard, their obligation to attend church services at their parish church was not met by their attending services within the Cathedral, since a cathedral does not have, by definition, a specific congregation.
The part of London where St Paul’s Cathedral was located included two parishes, St Gregory’s by St Paul’s and St Faith’s under St Paul’s. People who lived around the south, west, and east sides of St Paul’s Cathedral as well as people who lived south of the Churchyard (see space in yellow on the map above) attended St Gregory’s Parish Church, which was, literally, by St Paul’s, located adjacent to the Cathedral’s West Front, on the south side, also facing west.
St Gregory’s had special connections with the College of Minor Canons. Members of the College of Minor Canons often served as rectors of the congregation at St Gregory’s.
The Parishes around Paul’s Churchyard. Image courtesy Wikimedia Commons.
St Faith’s Parish Church was, literally, under St Paul’s, meeting for worship in the Cathedral’s crypt underneath the Choir of the Cathedral.
People who lived in the northeast side of Paul’s Churchyard, especially in the buildings that housed the bookshops, along with people who lived north and northwest of the Churchyard boundary (see space in orange on the map above) were members of St Faith’s Parish and attended church services in the crypt of the Cathedral.
Rectors of St Gregory’s Parish Church during Donne’s tenure as Dean included Simon Stubbs (until 1622), then Thomas Jennings (until the end of Donne’s tenure)
Rectors of St Faith’s Parish Church during Donne’s tenure included Martin Day (until 1624), William Woodford (until 1625), Finannal Smith (until 1625), John Lesley (until 1628), and Jonathan Brown (throughout the rest of Donne’s tenure). Brown was also a Prebend of Westminster Abbey.
The images below show Wenseslas Hollar’s engraving and a floor plan of St Faith’s Parish Church underneath the Choir of St Paul’s Cathedral.
St Faith’s Church. Image by Wenseslaus Hollar. Image courtesy the Wenseslaus Hollar Digital Collection, University of Toronto. 
Floor Plan, St Faith’s Church. Image courtesy Wikimedia Commons.