Hi
Follow the instructions here:
http://www.cic.gc.ca/english/information/applications/prcard.asp
Legal change of name
If your present name is different from the name printed on your Record of Landing (IMM 1000) or Confirmation of Permanent Residence (IMM 5292 or IMM 5688),
you must send in supporting legal documentation as proof of your name change in addition to supporting identity documents as requested in section 3 of Step 1. Supporting legal documentation may include:
a copy of a legal change of name document, court order, adoption order issued by a civil authority in a province or territory of Canada, or a marriage certificate, divorce decree, registration, declaration of union, revocation of declaration or annulment of union issued by a civil authority in a province or territory of Canada, showing your new name, unless you have been married in and are currently a resident of Quebec;
if you are a permanent resident who changed their name outside of Canada, provide a foreign passport or other national authoritative document that has been amended to reflect the new name, and an official document linking the old and new names.