In my country, there's this culture that every ramadhan people send those they love gift with notes "Happy Eid Mubarak", the gift can be food, cutlery, etc, are we able to do so?
I am thinking to do that, simply because I want to make them happy but suddenly I also think 'is it better to use the money for those who are in need who are struggling in poverty?' I also try to do sadaqa but i just want to give the people I love a ramadhan gift?

Is it something good to do? or recommended to do?

Yes you can do that, no problem. Of course you should also help the poor, but giving such gifts is permissible. As long as the gift is appropriate and makes others happy then yes it’s recommended