Vietnamese names are traditionally written family name first, then a middle name, then the given name: Nguyễn Văn Minh, Trần Thị Hương. The last word is the given name, and it is what people actually call you.
This is why a Vietnamese teacher, doctor, or elder is often addressed with a title plus the given name rather than the family name — "Chị Hương," not "Chị Trần." It can feel strangely informal to people used to Western convention, but it is the normal, respectful form.
A handful of family names cover an enormous share of the population. Nguyễn is the most common by a wide margin, followed by names like Trần, Lê, Phạm, Hoàng/Huỳnh, Phan, Vũ/Võ, Đặng, Bùi, and Đỗ. Sharing a family name with someone usually says nothing about being related.
Middle names historically carried gender information — Văn often appeared in men's names and Thị in women's — though this has become much less common in recent generations, and many families now choose middle names for meaning or sound instead.
Given names are frequently chosen for what they mean: Hương (fragrance), Minh (bright), Hùng (heroic), Thảo (respectful, herb), Anh (bright, elite), Linh (spirit). Many Vietnamese families abroad also use a Western first name alongside a Vietnamese one, which is its own kind of family history.