Algorithm to find Unique users from their transactions

Scenario

An eCommerce site allow users to purchase items without creating an Account. However, it captures following attributes from the Purchases based on the type of payment and type of delivery:

1. Name
2. Address
3. Email Address
4. Card/Account Number

Note: It is possible one type of transaction only get one subset of attributes (e.g. Name and Address) and another type of transaction get another subset of attributes (e.g. Name and Card Number)

Expectation

To offer customized products or to prevent Fraud, it want to find individual users.

E.g. It should identify following three transactions are done by single user:

1. name: Alice, email: [email protected]
2. email: [email protected], Card Number: 123456
3. name: Bob, Card Number: 123456 (Alice made purchase for Bob).

As you can see car-number/email is a stronger link than Name. So different attributes have different weights.

I have looked at couple classification algorithms (k-mean, k-mode..), but none of them is addressing this use case as I don’t want to classify users but identify individual users.

Is this a standard data science problem and which algorithm will best fit here? Thank you!