If you need to update the name on your permanent resident card, you are not eligible for a reissued card, and must apply for a new card. You can do so by filling out the PR Card Application (IMM 5445).
In addition to the identity documents requested in Step 1 of the PR Card Application, you will need to provide a copy of your Record of Landing (IMM 1000) or Confirmation of Permanent Residence (IMM 5292 or IMM 5688), as well as a legal document proving your name change (such as the Ontario Change of Name certificate).
If your name change document was not issued by a province within Canada, then you will also need to provide a provincial I.D. in the name requested (including a driver's license/photo card or a health card)