At home or outside of normal places, you would tell your first name to the strangers. That's fine, but is it the same for business or serious places?
No, it is not.
When went to my college management students' meet, it was confusing due to some of the fellows attached their first names only on badges. And more than one have same names. How hard it is to get identity.
It is very easy to guess many people share the same first name. Or same surname. But mostly nobody shares full name.
So tell your full name and earn identity to the ears of strangers.
Don't hesitate to tell your name. It is mostly unique and you can be identified easily and business needs your full name too.
Stop telling your only first name or surname.
Put your full name on badges or name boards.
Tell your name slowly if your name is difficult to pronounce or it has difficult spelling.
Note: All the text and images of this post is by @r-k-m