How can I change the email sender name from wordpress to (myblogname) on the "lost password" email?

When a user loses their password in wordpress, you are prompted to enter your email or username.

When the password reset email has been sent, it displays "wordpress" as a sender name. I want my website or blogname to replace that instead.

I would rather send my own personal email and link to the users my self, without sending anyone to the wp login page. On my website I have my own login page , and putting a lost password link their would fit me a lot better.

How can I have the "lost password" email that are sent to the users, display my blog name as the sender name , instead of "Wordpress" ?

Is it possible to have my own emails sent to the users that I can link to my login page thats on my site, not on the wordpress login page?