Does it matter to you if the name is pronounced differently in Bulgarian and English? I ask because I would only recommend Ivan and Damian if you’re okay with people using the English pronunciations. I know an Ivan from a South Slavic country and all his English-speaking colleagues call him EYE-vin. Likewise Damian will get DAY-mee-in rather than dahm-yan.
I like Yulian but I can see it getting mistaken for “Julian” in English because that’s a more familiar name.