When somebody subscribe to my website he receives this sort of e-mail

from WordPress <wordpress@******.com>
to ********@gmail.com
date 01.01.2001
subject [] Username and password
mailed-by ***.*******.com.**
[corrections are mine]

I would like the email the subscriber receives to convey my website info such as:
from admin@mywebsite.com
mailed-by MyWebsite.com

Any suggestions?
Thank you very much.

this is a function of the WordPress code, it's the same for any theme. You are going to have to look in the WordPress code or check the WordPress support forum. You might even look to see if there is a plugin that can change this.

Yes, there is a plugin

http://epicalex.com/new-user-email-set-up/

and it works on 2.7.1