The best replacement for card number is account number.

The best alternatives to card number are rated as following:
★★★★★  account number
★★★  alien number
★★  passport book number
★  passport number

Your alternative for card number is not listed? Suggest!
Speaking about card number, one probably shouldn't forget about detail.

Other search terms related to card number and their ratings are:
★★★★★ detail
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card number
account number
alien number