Do I have to tell the person it's zakat?

Your intention is enough

The Prophet Muhammad ﷺ said, "The reward of deeds depends upon the intentions" (Sahih al-Bukhari 1). For zakat, scholars require you to intend it as zakat at the time you give it, or when you set it aside for that purpose. The recipient doesn't need to know or agree to the label. So if you give your struggling cousin €300 intending zakat, it counts, even if you just say, "This is for you."

Protect their dignity

Many people, especially relatives and proud elders, find it hard to accept "zakat," because the word reminds them they're in need. Islam strongly warns against hurting people when giving:

Calling it a gift, giving it in an envelope, or sending it anonymously are all fine. See Should I give charity secretly or openly?

Do check eligibility

Not telling them doesn't mean not thinking. You still need reasonable confidence that the person qualifies, for example that they're poor, in debt or a stranded traveler, and that they're not your parent, child or wife. See Who can receive zakat? If you made a genuine effort and later found out they weren't eligible, many scholars say your zakat still counts, based on the hadith of the man whose charity reached a rich man by mistake (Sahih al-Bukhari 1421).

When it's worth mentioning

• If the person might refuse zakat on principle because they don't consider themselves eligible, a gentle word can help them decide honestly.
• If you're giving through a charity, they need to know it's zakat so they spend it correctly.
• If you're giving a large amount, a quiet word helps the person know it's meant to ease their need, not a loan they must repay.