Change '/user(/*)' URLs to 'profile(/*)' I want change all /user, /user/* urls by /profile, /profile/* urls. 
From a custom module, I copied all user routes (found in /core/module/user/user.routing.yml) to my custom .routing.yml file. I replaced all "user*" paths by "profile*". 

Now, I have the following. 

mycustommodule.register:
  path: '/profile/register'
  defaults:
    _entity_form: 'user.register'
    _title: 'Create new account'
  requirements:
    _access_user_register: 'TRUE'

mycustommodule.pass:
  path: '/profile/password'
  defaults:
    _form: '\Drupal\user\Form\UserPasswordForm'
    _title: 'Reset your password'
  requirements:
    _access: 'TRUE'
  options:
    _maintenance_access: TRUE

mycustommodule.page:
  path: '/profile'
  defaults:
    _controller: '\Drupal\user\Controller\UserController::userPage'
    _title: 'My account'
  requirements:
    _user_is_logged_in: 'TRUE'

mycustommodule.login:
  path: '/profile/login'
  defaults:
    _form: '\Drupal\user\Form\UserLoginForm'
    _title: 'Log in'
  requirements:
    _user_is_logged_in: 'FALSE'
  options:
    _maintenance_access: TRUE

mycustommodule.login.http:
  path: '/profile/login'
  defaults:
    _controller: \Drupal\user\Controller\UserAuthenticationController::login
  methods: [POST]
  requirements:
    _user_is_logged_in: 'FALSE'
    _format: 'json'

mycustommodule.login_status.http:
  path: '/profile/login_status'
  defaults:
    _controller: \Drupal\user\Controller\UserAuthenticationController::loginStatus
  methods: [GET]
  requirements:
    _access: 'TRUE'
    _format: 'json'

mycustommodule.logout.http:
  path: '/profile/logout'
  defaults:
    _controller: \Drupal\user\Controller\UserAuthenticationController::logout
  methods: [POST]
  requirements:
    _user_is_logged_in: 'TRUE'
    _format: 'json'
    _csrf_token: 'TRUE'

mycustommodule.cancel_confirm:
  path: '/profile/{user}/cancel/confirm/{timestamp}/{hashed_pass}'
  defaults:
    _title: 'Confirm account cancellation'
    _controller: '\Drupal\user\Controller\UserController::confirmCancel'
    timestamp: 0
    hashed_pass: ''
  requirements:
    _entity_access: 'user.delete'
    user: \d+

mycustommodule.reset.login:
  path: '/profile/reset/{uid}/{timestamp}/{hash}/login'
  defaults:
    _controller: '\Drupal\user\Controller\UserController::resetPassLogin'
    _title: 'Reset password'
  requirements:
    _user_is_logged_in: 'FALSE'
  options:
    _maintenance_access: TRUE
    no_cache: TRUE

mycustommodule.reset:
  path: '/profile/reset/{uid}/{timestamp}/{hash}'
  defaults:
    _controller: '\Drupal\user\Controller\UserController::resetPass'
    _title: 'Reset password'
  requirements:
    _access: 'TRUE'
  options:
    _maintenance_access: TRUE
    no_cache: TRUE

mycustommodule.reset.form:
  path: '/profile/reset/{uid}'
  defaults:
    _controller: '\Drupal\user\Controller\UserController::getResetPassForm'
    _title: 'Reset password'
  requirements:
    _user_is_logged_in: 'FALSE'
  options:
    _maintenance_access: TRUE
    no_cache: TRUE


From my website, when I go to the http://mysite/profile, I'm redirected to the correct page (the user view), but the URL change automatically to http://mysite/user. I want keep the URL as http://mysite/profile. How can I do that? Is it possible?
The routes you've defined are new routes with different names and this is the reason the standard routes are still in place. If you want to override the standard routes you would have to use the same route names like user.page:.

But this is not the best approach to alter multiple routes. Better use a route subscriber:

src/EventSubscriber/RouteSubscriber.php

&lt;?php

namespace Drupal\mymodule\EventSubscriber;

use Drupal\Core\Routing\RouteSubscriberBase;
use Drupal\Core\Routing\RoutingEvents;
use Symfony\Component\Routing\RouteCollection;

class RouteSubscriber extends RouteSubscriberBase {

  protected function alterRoutes(RouteCollection $collection) {
    foreach ($collection-&gt;all() as $route) {
      if (strpos($route-&gt;getPath(), '/user') === 0) {
        $route-&gt;setPath(preg_replace('/^\/user/', '/profile', $route-&gt;getPath()));
      }
    }
  }


  public static function getSubscribedEvents() {
    $events = parent::getSubscribedEvents();

    $events[RoutingEvents::ALTER] = array('onAlterRoutes', -250);

    return $events;
  }

}


mymodule.services.yml

services:
  mymodule.route_subscriber:
    class: Drupal\mymodule\EventSubscriber\RouteSubscriber
    tags:
      - { name: event_subscriber }