Two categories can have the same name (title) as long as they are not both parent (top level) categories and are not both children of the same parent category.
No two categories can have the same nicename (slug). If there is a collision when creating a child category, WordPress will append the slug of the parent to the slug of the newly created child category (child-name-parent-name). If there is a collision when creating a top level category a number will be appended to the end of the slug (category-2).