Hello, I have found out that the problem was not in alternative names, but in certificate chain. I had some extra certificates (not needed to verify my server certificate) in the chain file and that was breaking it.
-- S pozdravem Vladislav Kurz === WebStep, s.r.o. (Ltd.) ========= a step to the Web === address: Mezirka 1, 602 00 Brno, CZ, tel: +420 548 214 711 === www.webstep.net ======= vladislav.k...@webstep.net ===