Yes. This time of year it is a common occurrence.
BUT their is a particular process you must follow.
When you get to the payment screen and BEFIORE you pay you will see your address with an "edit" button next to it. Click that button and enter the new address.
ALSO be aware that if the gift is going to a more distant address then the shipping charges may change compared to what you are seeing. (Obviously a free ship item does not apply here). Shipping is based on BOTH weight AND distance.
If you do not change the address and then, after the fact, send the buyer an email asking to change the address the seller is within his rights to say no. Both Paypal and eBay offer seller protections BUT they only apply is the package is sent to the address on the screen. If it is a fairly inexpensive and common item I will accept the change. But as the item gets to be more and more expensive then I refuse. I am sure others feel the same way.
"Laissez-faire capitalism (AKA The Great Material Continuum) is the only social system based on the recognition of individual rights and, therefore, the only system that bans force from social relationships." ~ Ayn Rand
