Must a wife take husband’s last name for approval of a marriage-based green card?

No. While taking a spouse’s name (or hyphenating both names, otherwise combining them, etc.) is likely viewed somewhat positively by some reviewing USCIS officers, it isn’t a legal requirement or even a major consideration. USCIS will focus more on the degree to which you are sharing your lives together – combining finances and sharing legal obligations, spending time together and with each other’s’ family and friends as evidenced by photographs, and other indicators of a shared life.