JSFiddle - React, Tailwind, and code Playground

JavaScript

var existing_names = ['username1','username2','username3'];
var new_names = ['username1','username4','username5'];

function mergeArrays( a1, a2 ) {
    
    var len1 = a1.length;
    var len2 = a2.length;
    var found = false;
    
    for ( var x = 0; x < len2; x += 1 ) {
        
        found = false;
        
        for ( var y = 0; y < len1; y += 1 ) {
           
             if ( a1[y] === a2[x] ) {
                found = true;
                break;
            }
            
        }
        
        if ( ! found ) {
            
            a1.push( a2[x] );
            
        }
                
    }
    
    return a1;
    
}

// merge arrays
new_names = mergeArrays( new_names, existing_names );

// sort the resulting array
new_names.sort();

for ( var x = 0; x < new_names.length; x += 1 ) {
    document.write(new_names[x] + ', ');
}