Yes you can. You do not have to replace a resident alien card if it has no expiration date and was not issued before your 14th birthday.
The Customs were urging you to replace your card because the old cards are not tamper proof and if it was lost or stolen, someone could substitute a photo on it relatively easily.
The new cards have digital pictures, magnetic strips, and are technically far less able to be tampered with.
However, a new card has to be renewed every 10 years and it is nearly $400 in filing fee.
Do you mean if you hyphenbate you name on other documents, such as SSN, passport, driver license? Yes, those documents and a marriage certificate will generally prove you are one and the same.
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