Yes. Right after you reserve a wish, Wishpicks offers a box where you can add a short note. It's optional, and you can skip it.
One thing to know: the note isn't private from the owner. If they turn on reservations to see what's been claimed, your note shows up next to the reservation. So treat it as an optional message to the owner, and leave out anything that would spoil the surprise.
Steps
Open the wishlist link the owner shared with you.
Tap Reserve on the wish you want to give and confirm.
On the confirmation screen, type your note in the message box.
Tap Leave a message to save it. To skip the note, just close the screen.
About your note
The owner can read your note. Your note isn't hidden. The moment the owner turns on reservations, they see it alongside the claim. So don't write anything you'd rather keep a surprise.
Other gift-givers don't see it. People browsing the same wishlist can tell an item is reserved, but they can't read your note.
Don't put a delivery address in it. Wishpicks has no delivery-address feature. If you need to sort out where to send the gift, arrange that directly with the recipient, off-platform.
The note is optional — you can reserve without leaving one at all. Once it's saved, though, you can't edit or remove it, so take a moment to get the wording right before you save. Cancelling the reservation removes the note along with it. See "I reserved a gift by accident — how do I undo it?"