People who have birthdays that are close to Christmas often have to deal with people giving them one gift and saying it's for birthday and for Christmas. My birthday is a month after Christmas and I have had that happen. (Which is insane because my birthday is not even that close to Christmas) I say this is a bad idea because, to me, it trivializes your birthday. It's not necessarily about wanting more gifts, but rather wanting your birthday to be a separate, special occasion. So if you have a friend or family member whose birthday is very close to Christmas, if not on Christmas Day, try to make an effort to have their birthday be a separate celebration. They will appreciate it.
