Using different .inc files with same function names in .module file
You can use file key in your menu like:  

I assume you have a includes directory contain both files my_project_mobile_api.v1.inc and my_project_mobile_api.v2.inc and both files contain account_register function. 

Your hook_menu should be like the following.

function my_project_mobile_api_menu() {
  return [
    'api/v1/user/register' =&gt; [
      'page callback'   =&gt; 'account_register',
      'access callback' =&gt; 'user_is_logged_in',
      'type'            =&gt; MENU_CALLBACK,
      'file'            =&gt; 'includes/my_project_mobile_api.v1.inc',
    ],
    'api/v2/user/register' =&gt; [
      'page callback'   =&gt; 'account_register',
      'access callback' =&gt; 'user_is_logged_in',
      'type'            =&gt; MENU_CALLBACK,
      'file'            =&gt; 'includes/my_project_mobile_api.v2.inc',
    ],
  ];
}


You can also use 'file path' if you files not in the same module take a look at this example.