Your wife can keep her maiden name on all documents (Passport, Aadhaar, PAN). To prove your marriage for visa purposes (Canada/US), your Marriage Certificate is sufficient. You can also add your name as a spouse in her passport during its next renewal without changing her surname .
But if she chooses to change her name, she must update her Passport, Aadhaar, and PAN to ensure they match her new legal identity. The discrepancy with her educational degrees (which will remain in her maiden name) is very common and is legally resolved using a “Same Name Affidavit” or the Marriage Certificate.