Francis Hyde explains that one of the fields extended from Stony Stratford to the mill drive and was bordered to the south by the Wolverton Road. Thus all the fields named Rylands - a good giveaway to the arable properties of the soil - were in this field.
The second field was to the south of the Wolverton Road, starting at the corner turn and encompassing Barr Piece and Barr Close, Marron Fields, Dean's Close, Roger's Holm and Lower Slade. This, as you can see from the overlay, is mostly covered by the Railway Works, McCorquodale's and the 19th century town.
Barr (OE baere) means barley and plainly takes its name from what was grown there. It is likely that the name Atterbury, often found in Wolverton and area, can trace its origin from this or a similar named field in the area. When surnames originated in the 14th century people were quite as likely to take thier name from the place where they lived. Thus John atte Barre (John at the Barley Field) became in time, Atterbury.
I am not certain of the origin of Marron, but it may possibly come from the Old English maere, meaning great