When a married couple is sending informal correspondence such as a greeting card or letter, there is no steadfast etiquette rule for whose name should be written first in the signature.
Usually, the person writing the note writes their name last.
Some people feel the woman’s name should always be first.
Others believe the man’s name should be first to follow the “Mr. and Mrs.” format.
If the names of children are included in the signature, the father’s name is first, followed by the mother’s name, and then the children’s names.