Support, encourage, or pressure? I feel all three in your question. Regardless, for a couple in USA, a woman can keep the maiden name, take the husband's name, hyphenate the names, her partner can take her maiden name or the hyphenated name, or both can select a different surname altogether and change to that legally if a court agrees.
Keeping a maiden name after marriage still bothers some other family members in the early 21st Century. However, I think that in some cultures, the woman has never changed to the husband's surname. I would like to find out how many people in USA are bothered by a lack of name change by others after a marriage.