Let user select their own category

User taxonomies can help you achieve this, I’m working on something similar.
You can install the plugin http://wordpress.org/plugins/user-taxonomies/, and register a custom taxonomy , although in my case the plugin has some limitations, may be it helps you.

register_taxonomy('profession', 'user', array(
'public'      =>true,
'labels'      =>array(
    'name'                        =>'Professions',
    'singular_name'               =>'Profession',
    'menu_name'                   =>'Professions',
    'search_items'                =>'Search Professions',
    'popular_items'               =>'Popular Professions',
    'all_items'                   =>'All Professions',
    'edit_item'                   =>'Edit Profession',
    'update_item'             =>'Update Profession',
    'add_new_item'                =>'Add New Profession',
    'new_item_name'               =>'New Profession Name',
    'separate_items_with_commas'=>'Separate professions with commas',
    'add_or_remove_items'     =>'Add or remove professions',
    'choose_from_most_used'       =>'Choose from the most popular professions',
),
'rewrite'     =>array(
    'with_front'              =>true,
    'slug'                        =>'author/profession',
),
'capabilities'    => array(
    'manage_terms'                =>'edit_users',
    'edit_terms'              =>'edit_users',
    'delete_terms'                =>'edit_users',
    'assign_terms'                =>'read',
),
));

Update

I’ve compiled a similar plugin User Tags which might help you.

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