As I already said in my comment Czech language doesn't have a standardized list of month name abbreviations. That is most probably the reason Microsoft chose to use roman numerals for MMM format. But you create your own format to support short month names.
var czechCulture = new System.Globalization.CultureInfo("cs-CZ");
var customDateTimeFormatInfo = (System.Globalization.DateTimeFormatInfo)czechCulture.DateTimeFormat.Clone();
var czechMonthAbbreviations = new [] {
"led.","úno.","bře.","dub.","kvě.","čvn.","čvc.","srp.","zář.","říj.","lis.","pro.",""
};
customDateTimeFormatInfo.AbbreviatedMonthNames = czechMonthAbbreviations;
customDateTimeFormatInfo.AbbreviatedMonthGenitiveNames = czechMonthAbbreviations;
DateTime.Now.ToString("dd MMM yyyy", customDateTimeFormatInfo).Dump();
These abbreviations should be understandable but be aware this is not how you would write date in Czech. Technically you should set the genitive form as well but trying to squeeze that into 3 letter would produce something like "čce." for July which would make the reader think hard at first and then roll his eyes.