Should we make a tag for the hat as well and attach it to it? I guess there mainly would be info on the yarn used for this.

Yes, definitely.
A tag can tell about yarn(s), needles, cast on, any special techniques used; it also identifies *you*.

Makes sense. Thank you, Mt. Mom.

Thank you for this question - I hadn't thought about tagging the hat, but it makes perfect sense that I should, now that you put the thought into my head.