A complete name

A name within a name,
Where alphabets follow one another
Through this journey called life
Have you ever realized?
In your name is my own
And in mine is yours?
The first letter in yours
Follows the first of mine
And second of mine
Does not leave
The very first of yours…
Imagine then,
What would be
If one of them was taken away
A name there wouldn’t be,
Only an incomplete word
That meant nothing
Put the two letters of your name
Along with two letters of mine
See, what you find?
Another complete name!