There is Czech version of Luke, however. Seeing how the lands of Bohemia have been historically Catholic, it is to be expected that so important a Saint as one of the gospel writers would have a Czech version of his name. Lukáš. Vocative case would be Lukáši. https://cs.wiktionary.org/wiki/Luk%C3%A1%C5%A1
My Czech teacher told me that 'otec' is a formal word that you don't use anymore. He said you would use something like 'tatka' instead. Is that true???
No. "Otec" is a formal word, but it was not replaced by its less formal synonyms. There are situations for each.
Try counting internet hits under various categories for phrases like "její X je", where X is whatever you want to compare. The "její" blocks false positives from Slovak. I did not see false hits from other languages with it in.
"Otec" is usually used in formal situations or as absolutely neutral word (not slowing any feelings between the two). If you want to display that they are close to each other, you can use informal word "táta". Saying "taťka" you either express really strong link between the two. Therefore I would translate "otec" as "father" (btw. even in the Church meaning), "táta" as "dad" and "taťka" as "daddy". More rarely you can hear the word "taťka" in a bit dishonesting meaning - a man who gets older, is loosing his previous drive and interested in his house/family/... more than friends, parties, ... Compare with the meaning of "Dad" in "Dad's army" - the nickname for the Home Guard of the UK during WWII. So yes, "otec" is rather formal, but definitely it has its place in the live language.