Hello,

Yes , It is must. If you have the surname in your legal documents like passport, birth certificate, etc. You must furnish your full name as you want it to appear on your passport. and While filling the online non-immigrant visa application (DS-160), the surname field is mandatory.

But in some countries where people don't use surname on birth certificate but there's way they can inform the other authorities about it.

All the best!

Hope it will help!

Thank you!