To me...
Senario -1
if you know him/her who gives you the gift in a way. (a friend , a family member ...)
the gift is yours any more :)
but if you dont accept and giver insists so you can give the gift to another one (if it is possible).
Senario -2
if you dont know him/her who gives you the gift
the gift is not yours
it belongs to giver.