How to make SQL Server find a login matching the name provided?

Please make sure you have selected "SQL Server Authentication" mode for user you created from Server > Security > Logins option.

Another possibility, is that you created the SQL Server login using Management Studio, and the option requiring the user to change the password on first login was checked. If you didn't immediately login with Management Studio, and change the password, then the attempt to login from the other machine is not able to pop up a dialog box to change the password and so it fails.

try it by removing user and create again.