What is the correct format in naming your newborn child? I understand that different cultures have different way of naming the child. For example in Arab culture naming is different than in Pakistani culture.
Back home, in Pakistan, when the child is born, he/she is given a name and then the father's first (just first name) name becomes child's last name. For example: Father: Muhammad Akram Bashir (Akram is the given name). If a boy child is born, his name would be:
Child: Muhammad Hamza Akram (Hamza is the given name, and father's first name becomes child's last name, i.e. Akram). This is the tradition back home. Is it correct Islamic way?
My question what is the correct ruling? Since we will be called by our first name and then our father's name on the Day of Judgment, therefore it would be helpful for many people to know the correct procedure and ruling of naming a child.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

A Muslim should not carry a compound name the first part of which indicates seeking blessing and the second part of which is to be a proper name. This was the practice of the non-Arab polytheists; hence a Muslim is supposed to not imitate them even if he is a non-Arab Muslim. The reason behind this prohibition is the confusion that may be caused by such compound names.

As for calling people by their first and second names on the Doomsday, it is correct as reported in Saheeh Al-Bukhaari no matter whether it is a compound or a single name. Those people who have names that are composed of two or more parts, will be called by the very names they were called by in this worldly life along with their father's names.

For more benefit on naming children with good names, please refer to Fataawa 82724, 87262, 88553, and 87596.

Allah knows best.