Yes, you can give to any needy person. But please know that the 2.5% once a year ZAKAT is a non-Qur'anic, "Imamist" concoction. You will not find 2.5% in the Qur'an. Give them whenever you earn income and whatever is beyond your needs.
ZAKAT = Growth & Development of the 'self' and the society.
2:219 ----. And they ask you what they should give. Say, "All that is surplus." Thus God makes His messages plain for you, that you may reflect.
6:141 He is the One Who creates bounties for you, such as gardens that are cultivated, greens that are wild, palm trees of various kinds, crops in diversity, olives and pomegranates, fruits that are similar and diverse. Enjoy them, but give Him His Right on the Day of the Harvest. And waste not the bounty of God. He does not love the wasteful.
[‘give Him His Right’ = Give God His Right = Render to the poor what is their Divinely ordained right. Time to reflect on Zakaat and Sadaqaat: See 2:3, 2:219, 9:60, 11:64, 55:10]