Technically, the merchant is only "supposed" to check to make sure the signatures match, or if the card is not signed, to match up the names.
Many people write "see ID" on the back in the hopes that the merchant will ALWAYS ask for an ID, in case the card is lost or stolen. My husband has this on his, and an ID is still only asked for about 40% of the time.
I do sometimes use my "husband's" debit card (we don't use credit cards at all), not because i'm spending "his" money, but because we share a bank account, and for some reason, our bank refuses to issue a card with my name on it (makes no sense because it's a joint account with both names on the statements and the checks, but whatever; it's something i need to look into simply because it's a inconvenient). Usually when they ask, i show my own ID, and sign the slip with my first initial (it's the same as his middle initial) and our shared last name, because i figure i have less to explain that way. 90% of the time it's no problem; they either don't notice, don't care, or figure we're married and share a card, no big deal. But occasionally they won't take it without his signature, so i'll either write a check, or simply take my business elsewhere if they won't accept them.