What is this symbol "Dy" called (see image)
I think it's a stylised "fr", standing for "from", a common term used when signing a card.
The initial upstroke, downstroke and curve form a cursive lower-case 'f', and the remaining piece that looks like a '7' forms a cursive 'r'.
It's a heart. She is signing their names but instead of writing "Love," for the closing, she drew a heart.