as usual, there are different versions: I would suggest to try a Google search
Based on a Google search (over 130,000 hits): "The name is French in origin. The original French spelling of Rayment is Raymond. This is probably why some changed the French spelling of Rayment, to the English spelling of Raymond. Some retained the French Rayment spelling, and yet can be proven to be directly related to those who used the Raymond spelling. Record keepers made errors when recording legal documents. Because pronunciations were different and people could neither read or write, they recorded names as they sounded rather than using a common accepted standard spelling. Other variations have appeared because of this, such as: Raimond, Raiment, and Raymont." Source http://homepages.tesco.net/~rayment/history.htm
Another site http://privatewww.essex.ac.uk/~alan/family/S-Raymond.html says
The origin of the name Raymond
English and French: from the Norman personal name Raimund, composed of the Germanic elements ragin + mund counsel + protection.
Cognates: Catalan: Ramon. German: Raimund, Raymund (Austria), Reimund, Reinmund. Italian: Raimondi, Raimondo, Ramondi, Ramondo; Ramundi (Southern Italy); Rimondi (Emilia). Portuguese: Raimundo. Spanish: Ramón.
Diminutives: French: Remondeau, Remondon. German: Reim. Italian: Raimo; Ramondelli, Ramondini, Ramondino, Rimondini. Provençal: Ramondenc, Ramondou, Ramonenc, Ramonic, Raymonenc, Raymonencq.
Patronymics: Irish: Redmond, Redmonds (Erse Mac Réamionn).
Variants: English: Raiment, Rayment, Raymont. French: Raimond, Ramon, Ramond, Reymond, Rémon, Rémond, Rémont.
About the origin of the name:
RAYMENT (British). "Might/counsel protector".
I give you two more web sites in reference, but there is much-much more!
Local time: 20:35
Native speaker of: Hungarian
PRO pts in pair: 123