connesction string adjustment

Question

I have a problem with connection string ;
when the application wants to connect(ms sql serever), it shows this disturbing error
<< login failed for user ...>> or somthing like it that depends on connection string
 

As you know each computer has a different name ,
I've create the user name and pass( sql ) on client computer (should i do this for each client?)

,but the error occurred.

what do you suggest to fix it, and runs on each computer?