Hide Updates from Admins that don’t equal a set Username

You could try following:

$current_user = wp_get_current_user();
if( user_can( $current_user, 'main-admin' ) ) {
    // Do your stuff
}

For more info please read in the Codex about:
user_can , wp_get_current_user

Edit: my mistake, was reading wrong, I thought you meant a custom role main-admin.
Not to make my mistake suddenly as correct, but maybe you create a role where the user belongs to. (is maybe even easier to manage?)

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Add-on Trying to give an correct answer/option now.

There are several ways/options to achieve your goal below are 2:

Knowing the name makes it able to use: get_currentuserinfo()

global $current_user;
get_currentuserinfo();
if ( $current_user->user_lastname ) {
    // Do your stuff
}

Codex: get_currentuserinfo

When you know the user id you could use get_current_user_id():

$user_id = get_current_user_id();
if ( $user_id == 5 ) {  // add correct id
    // Do your stuff 
}

Codex: get_current_user_id

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As mentioned you can also create a custom role with administrator caps, which is explained here by @RutwickGangurde. To keep the answer here complete I added the code here.
NB: The setting is saved to the database (in table wp_options, field wp_user_roles), so it needs to run only once

I personally use a Class in functions.php to be sure a certain function only runs once, which in this case is a must!
Add both functions into your functions.php (make first a copy!)

class run_once
{
    function run( $key )
    {
        $scenario = get_option( 'run_once' );
        if ( isset( $scenario[$key] ) && $scenario[$key] )
        {
            return false;
        }
        else {
            $scenario[$key] = true;
            update_option( 'run_once', $scenario );
            return true;
        }
    } // end function
} // end class

// Now use the class with this function (which will only run once!)
$run_once = new run_once;
if ( $run_once->run( 'cloneRole' ) )
{       
    function cloneRole()
    {
        global $wp_roles;

        if ( ! isset( $wp_roles ) )
        $wp_roles = new WP_Roles();

        $adm = $wp_roles->get_role( 'administrator' );
        //Adding a 'new_role' with all admin caps
        $wp_roles->add_role( 'main-admin', 'Main Admin', $adm->capabilities );
    } // end Function
    add_action( 'init', 'cloneRole' );    
} // end if(..)

Core info about add_role

You can now add users to this custom role and use that role in other situations as in:

$current_user = wp_get_current_user();
if( user_can( $current_user, 'main-admin' ) )
{
    // Do your stuff
}