Monogram question

ArcticFox

Not sure if this is really a monogram.. but you know how you can buy thank you cards with an initial on it?  Would that be for your first or last name?

I'm doing thank you for DD's bday party - so would I do her last initial?  I think I'm thrown off because I still use my maiden name.. but then too, for a kid I feel like I'd use their first initial even though the cards are prob meant for their last name?

What do you do?