How to set a validation constraint for base fields like the taxonomy term name?

I'm having trouble setting a validation constraint on the name of the taxonomy term.

function MYMODULE_entity_bundle_field_info_alter(&$fields, $entity_type, $bundle) {
  if ($entity_type->id() === 'taxonomy_term' && $bundle === 'my_taxonomy_type') {
    kint($fields['name']);
    if (isset($fields['name'])) {
      kint('found name');
    }
  }
}

When I rebuild the cache with drush, kint() outputs the value of $fields['name'] as null.

When I use kint() to output the value of $fields, I see this:

array (4) [
    'parent' => Drupal\Core\Field\BaseFieldDefinition (7) (
        protected 'type' -> string (16) "entity_reference"
        protected 'propertyDefinitions' -> null
        protected 'schema' -> null
        protected 'indexes' -> array (0) []
        protected 'itemDefinition' -> Drupal\Core\Field\TypedData\FieldItemDataDefinition (3) (
            protected 'fieldDefinition' -> Drupal\Core\Field\BaseFieldDefinition (7) RECURSION
            protected 'definition' -> array (2) [
                'type' => string (27) "field_item:entity_reference"
                'settings' => array (3) [
                    'target_type' => string (13) "taxonomy_term"
                    'handler' => string (7) "default"
                    'handler_settings' => array (1) [
                        'target_bundles' => array (1) DEPTH LIMIT
                    ]
                ]
            ]
            protected 'typedDataManager' -> null
        )
        protected 'definition' -> array (7) [
            'label' => Drupal\Core\StringTranslation\TranslatableMarkup (5) (
                protected 'translatedMarkup' -> null
                protected 'options' -> array (0) []
                protected 'stringTranslation' -> null
                protected 'string' -> string (12) "Term Parents"
                protected 'arguments' -> array (0) []
            )
            'description' => Drupal\Core\StringTranslation\TranslatableMarkup (5) (
                protected 'translatedMarkup' -> null
                protected 'options' -> array (0) []
                protected 'stringTranslation' -> null
                protected 'string' -> string (25) "The parents of this term."
                protected 'arguments' -> array (0) []
            )
            'cardinality' => integer -1
            'provider' => string (8) "taxonomy"
            'field_name' => string (6) "parent"
            'entity_type' => string (13) "taxonomy_term"
            'bundle' => string (18) "my_taxonomy_type"
        ]
        protected 'typedDataManager' -> null
    )
    'field_int_count' => Drupal\field\Entity\FieldConfig (35) (
        protected 'deleted' -> boolean false
        ... cut
        protected 'id' -> string (56) "taxonomy_term.card_group_private.field_term_date_created"
        protected 'field_name' -> string (23) "field_term_date_created"
        protected 'field_type' -> string (8) "datetime"
        ... cut

"taxonomy_term.card_group_private.field_term_ref_author" protected 'field_name' -> string (21) "field_term_ref_author" protected 'field_type' -> string (16) "entity_reference" ]

The name field is nowhere to be found. How can I add a constraint to taxonomy term names?

Field name in taxonomy is a baseField not a bundleField so you should rather use HOOK_entity_base_field_info_alter instead to add custom definition to it