While most common approach is to use Model::select, 
it can cause rendering out all attributes defined with accessor methods within model classes. So if you define attribute in your model:  
<?php
namespace App;
use Illuminate\Database\Eloquent\Model;
class User extends Model
{
    /**
     * Get the user's first name.
     *
     * @param  string  $value
     * @return string
     */
    public function getFirstNameAttribute($value)
    {
        return ucfirst($value);
    }
}
And then use: 
TableName::select('username')->where('id', 1)->get();
It will output collection with both first_name and username, rather than only username. 
Better use pluck(), solo or optionally in combination with select - if you want specific columns. 
TableName::select('username')->where('id', 1)->pluck('username');
or 
TableName::where('id', 1)->pluck('username');  //that would return collection consisting of only username values 
Also, optionally, use ->toArray() to convert collection object into array.