William Peche
The family name of Peche is mentioned in the Domesday Survey. One of the records also references Belchamp Walter (Thunderlow).
The geni.com page for Guillaume de Péché, I
There is a lot of information on this page and although there is a button that when pressed encourages you to join Geni, there are quite a few "curators notes". These will have to be pursued further but the first I have extracted from them is the reference to Aubrey de Vere as a "progenitor of the earls of Oxford".
I don't have a problem with that Aubrey was the "progenitor of the earls of Oxford" but I am less sure that Peche was an undertenant of his at the time of Domesday.
Rishbridge, Suffolk
Rishbridge is not far from Hinkford, the current location of Belchamp Walter, the communities of Clopton and Dalham are located in Rishbridge. Gestingthorpe is also in Hinkford.
Progenitor of the earls of Oxford
This statement comes from the notes on the geni.com page for Guillaume Pecche (I will have to check was the source for this was),
Enisant <h;of Belchamp>
Again, this shows a deficiency with the recording of Domesday in a database.
Enisant could be just another term (Old English/Nirman/Latin) for undertenant (underlord) to the tenant-in-chief. It may not be an actual name. The way that it is displayed in OpenDomesday is with <> brackets, this is not clearly explianed. The map of the location is the same as it is for Belchamp Walter and there is no additional information on the OpenDomesday page.