I believe the answer is:
My name is heard from the beginning of time.
beginning of time
Where to search for me?
Well, you can find me when you log in, watch closely.
you can find it quite easily when you log in
I am original, indeed;
I am original
my reflection is seen in the night light.
night light has gin backwards, its "reflection"
Obtained by mixing ingredients, all the engineers need me...
Mixing ingredients, engineers, both contain "gin"
Although you will not find any traces of me in a cup of coffee!
There is no "g", "i" or "n" in a cup of coffee.
and unless you spike it, a cup of coffee shouldn't have gin in it :P
As for the title:
Shh! I'm supposed to be incognito