Hi @bee hurf
Unless someone else on here has an alternative approach, I think you will need to use a gift app that integrates with Klaviyo.
The Shopify placed order event pushes to Klaviyo the billing name & address (the giver) and shipping name & address (the recipient). However this doesn't help in your use case as I don’t think there will be an event property in Klaviyo that says it’s a gift.
That’s where a gift app that integrates with Klaviyo comes in. It will send specific gift events to Klaviyo. The additional benefit is that the gift option will be on the product page so the buyer can see that upfront and add their message before proceeding to checkout. Most also have a nice feature to set the time of a message to be sent to the recipient notifying them that they have a gift. Useful for upcoming birthdays.
Here’s one I came across for Shopify https://giftnote.com/ and demo site here https://demo.giftnote.com/ and their Klaviyo integration here https://giftnote.com/blog/supercharge-giftnote-with-our-klaviyo-integration. Costs $1 USD per order, but there will be others out there.
Hope that helps
Andy