The name on your PR Card is based on the name on your Confirmation of Permanent Residence (COPR) which, in turn, is based upon the name on your passport when you “landed,” i.e. began a permanent resident. So, if you want to change your name on your Pr Card, you’ll have to change it on your COPR, which means changing it on your passport or demonstrating that it is not your middle name on your passport, but your maiden name.
If you don’t want to change it, then you’ll have to use your ID as it is. But you can omit your “middle” name when asked for your given name. Many people do unless the form asks for your middle name.