According to the passport with an old surname you can go only to the visa-free countries .For Russian citizens traveling to Tunisia through a travel agency for up to 30 days and arriving in the country by direct flight, a visa is not required..The stamp on entry is put on arrival at the airport, the immigration card is also filled on the spot .In order not to have any questions, together with the existing internal passport for the maiden name, you must have a certificate of marriage - within 30 days after the change of the surname the passport of the citizen of the Russian Federation remains valid .

Otherwise, first you will need to get an internal passport of the Russian Federation. It is done within 1, 5 - 4 weeks after submission of the application. For replacement, you need a marriage certificate, a receipt for the payment of a state fee of 200 rubles, 4 photos 3, 5 * 4, 5, an old passport.