Originally I am from Romania and my native language is Hungarian. My name is thus a fairly typical Hungarian name.
László is one of the most frequent Hungarian first names. There exist families that have it as a last name, although "last" and "first" can be tricky sometimes (see below ;) and there was at least one (in)famous László László. The acute accents indicate longer vowels. The consonants s and z together denote a single sound similar to English s, as in "dislike" (a single s in Hungarian would be pronounced like English sh). The pronunciation is thus something like "Laasloo", or "last-low" in British accent but without the "t". Lazlo is a common misspelling. The name derives from the Slavic Vladislav present in various forms in many different languages. Here is a short list of famous bearers of the name. Saint Ladislaus (1040-1095) was an early king of Hungary. His cult-like popularity during the Middle Ages is the main reason for the frequency of the name until today.
Kozma is a relatively common family name as well. Besides Hungarian it appears in different spellings in many Slavic languages and in Romanian. In some languages it can be a first name and it is related to Cosima. Ultimately it might be of Greek origin. Saint Cosmas and Damian were wandering physicians in the 3rd century AD.
Hungarian names are often written family name first, according to eastern name order.
Some people with the same name (unrelated to me):