I have recently installed OS X version 10.9 on my MacBook Pro. When I start it, it doesn't require any password but when I try to install Adobe Flash Player or other plugins I am asked to approve the installation by entering the password of the user who is now "Us" (different name). When I enter the old password I had before formatting and installing new OS X, it kept saying wrong password. Is there any standard password to use?
You need to open the Users & Groups section of the system preferences and check what users are available. Is there one with admin privileges? Use that for the installation dialog. The inconvenience will be that in those dialogs you will need to enter the admin user name in addition to the password.
If there is no admin user, you could try to enable a root account. However, this needs admin privileges to be set up. Check if the padlock icon in the lower left corner of the Users & Groups section is closed (needs password, click on icon to open the password dialog), or open (you are free to add accounts). If the padlock icon is closed and you do not have any working admin user - password combination, I recommend to re-install OS 10.9 and to add the admin user at the appropriate prompt in the installation process. I hope this won't be needed - this should really be your last resort.
For Apple's explanation of the root account setup, see this article.