Do I have to give up my culture to become Muslim?

Islam is not one culture

Islam isn't Arab, Pakistani or Turkish culture. Muslims live in Nigeria, Indonesia, Bosnia, China and Brazil, and each place has its own food, dress and customs. You can be a British, French, German or American Muslim. See Is Islam only for Arabs?

The Quran even describes our differences as something meant for us to appreciate:

The rule: keep the good, drop the harmful

Scholars have a well-known principle that local custom is respected in Islamic law unless it contradicts a clear text. In practice:

• Keep: your name (in most cases), your language, family recipes made halal, sports, national holidays like Bonfire Night or the Fourth of July in their non-religious form, your sense of style within modesty.
• Adjust: pub nights become coffee nights, pork dishes get halal versions, and party clothes get a little more modest.
• Drop: alcohol, gambling, religious rituals of other faiths, and anything that involves clear sin.

Even your name usually stays. See Do I have to change my name after becoming Muslim?

The Prophet ﷺ respected cultures

The Prophet ﷺ let people from Abyssinia (Ethiopia) perform their traditional spear display in his mosque on Eid while his wife Aisha watched. He didn't ask the Abyssinians or the Persians to become Arabs; he asked them to worship Allah alone and be good people.

Watch out for "culture swap" pressure

Some converts feel they must dress, speak and eat like the community at their local mosque. You can enjoy other Muslim cultures, but you don't have to adopt them to be a "real" Muslim. Your culture can bring something fresh to the ummah, and Muslims from other backgrounds will understand you better for it. Mixed families are part of this too. See Can I marry someone from a different race or culture as a Muslim?