der Nachname
last name
A person's family name, which is usually given after the first name and indicates belonging to a family.
Bitte geben Sie im Formular Ihren Vor- und Nachnamen an.
Please enter your first and last name on the form.

last name
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last name
A person's family name, which is usually given after the first name and indicates belonging to a family.
Bitte geben Sie im Formular Ihren Vor- und Nachnamen an.
Please enter your first and last name on the form.

The word consists of 'Nach-' and 'Name' (name). The prefix 'Nach-' means 'behind' or 'afterward'. So the 'Nachname' (last name) is the name that comes after the first name.
In Deutschland steht der Nachname meistens hinter dem Vornamen.
In Germany, the last name usually comes after the first name.
'Nachname' (last name) is very often used in the fixed combination 'Vor- und Nachname' (first and last name), especially on forms, during registrations, or when introducing yourself officially.
Tragen Sie bitte Ihren vollständigen Vor- und Nachnamen ein.
Please enter your full first and last name.
The word 'Nachname' (last name) is often used in formal or official situations. A typical question in government offices or during registration is: 'Wie ist Ihr Nachname?' (What is your last name?).
Die Dame am Schalter fragte mich nach meinem Nachnamen.
The lady at the counter asked me for my last name.
name
'Name' and 'Nachname' both refer to what a person is called. 'Name' is the general word and can mean the full name, that is, first name and last name together. 'Nachname' is only the family name, for example 'Müller' in 'Anna Müller'. The words are especially easy to confuse on forms or at appointments. If only 'Name' is written there, it often means the full name. If 'Nachname' is written there, you should write only the family name.

Morgen schreibe ich meinen Nachnamen auf das Schild an der Tür.
Tomorrow I will write my last name on the sign on the door.
Lisa sagt ihren Namen langsam, damit die Ärztin ihn richtig schreibt.
Lisa says her name slowly so that the doctor writes it correctly.