insert autofocus in a custom taxonomy form

You can use wp_register_script() then wp_enqueue_script() to inject javascript into wp admin.

functions.php or plugin (my personal recc would be a simple plugin):

wp_register_script( 'focus-tag-name-script', 'path/to/script.js' , 10 );
wp_enqueue_script( 'focus-tag-name-script' );

script:

jQuery( window ).on( 'load', function() {
    jQuery( 'input[name="tag-name"]' )
        .focus() // place cursor in field
        .select(); // select field contents
} );

As requested in the comments, here it is as a plugin:
(I just wrote this out here without testing, but at the very least should put you in the right direction if there are any errors)

// define the plugin
jQuery( function( $ ) {
  $.fn.fieldFocus = function( options ) {

    var settings = $.extend({
        select: false
    }, options );

    this.focus() // place cursor in field
    if ( settings.selectContents ) this.select(); // select field contents
  } );
} );

// calling the plugin
jQuery( window ).on( 'load', function() {
  // places cursor in the field
  jQuery( 'input[name="tag-name"]' ).fieldFocus();

  // places cursor in the field and selects contents
  jQuery( 'input[name="tag-name"]' ).fieldFocus( {
    selectContents: true
  } );
}