Sorry for long delay ... the first recorded Bayman (that is, my family) I have found is in Ramsbury Wiltshire 1533 and they record their name as Bayman als (short for "alias"; Americans use aka short for "also known as") Pytthouse. The family used this for at least two hundred years with a number of variations including Pithouse, Pittis and Pittes. It was common in medieval times to use another name as an alias ... some reasons are to 1. associate with a prestigous family 2. Use the name of of your wife if she came from a prestgous family 3. could also imply that the person was illegitimate and the second name was the real fathers name.
I have searched far and wide and have not been able to find records before 1533 that indicate where the Pytthouse came from. There is a place called Pythouse in southern Wilthire which was owned by a well known family called Bennett and I have found one example of where they called themselves Bennett als Pythouse but have found no connection so far.
I have also examined the possible connection with other variations of Pytthouse such as Pittis, Peytows, Peyto etc but to no avail. There is a book by a Pittis family member (Pittis Genealogy, 1945) which lists members from 1480 to 1944 and there are many early variations on the spelling of their name - Pyts, Pyttys, Pitts, Pits, Pittes, Pyttis etc
If we all get our DNA tested then we will be able to link up with the papers records...you will find my test results at
http://www.worldfamilies.net/surnames/b/bynum/results.html - I am trying to find the origin of Bayman as being derived from either the Baynhams of Gloucestershire or the Beaumont family.