GOOD NAME

"What is your good name" !  The first time I was asked this, I was bewildered as to what they were asking for...!  I hope I have a good name for reliability and punctuality....!  But, what is my good name ?  So now I give them my 'first name', but perhaps it's my surname, which is my 'good name' ?  Is my first name more good than my surname ?  Now that's a question....I thought this form of address was used only in India, but talking to someone from Bahrain on the telephone a few days ago, I was freshly taken aback when I was asked, in a heavy Middle Eastern accent, what my good name was !  Now I wonder if my 'good name' in  Bahrain is different to my 'good name' in India ?