What is the exact procedure to choose a name or starting alphabet? I mean what factors needs to be considered such as day/date and time of birth? Please enlighten.

There is no specific procedure for choosing Islamic names. People simply choose what they like and what seems most meaningful to them. Some people like names related to beauty, others names related hope, or names related to God's mercy. For other people it depends on both meaning and the letter it starts with.

Some Muslims choose names based on how it sounds in their geographical location. Thus they may choose Ryan or Judy if they live in the United States or Britain because these names fit in easier.

Some people think date and time of birth should affect what names you choose. But there is no true system for this, it is all folk belief and bias and differs from one culture to another.