Onomastico, ‘name day’, the celebration of the name associated to your name. Normally the feast day of the Saint after whom you are named.
Pretty much like a birthday, you can got a card, flowers, maybe not gifts but you will certainly spent some time with your family and friends.
If you are lucky and your name is Giovanni, or Teresa, you can celebrate more than one onomastici in a year!
if you have a double name, such as Maria Teresa or Gian Paolo you are allowed to celebrate twice.
As we say ogni scusa è buona per festeggiare (‘any possible excuse to celebrate’!)