Do you include the hoop with each finished piece when gifting?

This might be a silly question but I’m just starting out my embroidery journey so I apologize in advance!

I’m just wondering if you plan on giving someone an embroidery piece as a gift to frame, do you always include the hoop? Or can you finish the piece off with a felt backing and take it off the hoop? From videos online it seems that everyone just includes the hoop with the actual piece. Are they supposed to hang it on the hoop? Looks odd to me with the screw on top??

Just wondering if I need to buy a bunch of hoops if I’m going to be giving one away each time I gift a piece to someone.

Thank you!