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Julius Caesar's name is spelled with J both in Latin and in English. So is Julia the Elder. There are plenty of examples of Julia in English, see https://en.wikipedia.org/wiki/Julia
I think this applies to Jurij (Yurij) and other names that begins with Ju as well.
Why is Y often used when J is a very established spelling, which is used in e.g., German and Scandinavian languages?
English speakers typically pronounce "Julius Caesar" and "Julia" with the sound /d͡ʒ/, like in the English word "jam".
It's true that in various European languages, including German and Scandinavian languages, J is an established spelling for the sound /j/ (like in the English word year or the German word Jahr). And English speakers may use that spelling and pronunciation in words or names that are spelled that way in the original language, such as someone named Johann in German or Jan in Swedish.
But that convention, although not completely unfamiliar to English speakers, is not the most common interpretation that English speakers tend to give to the letter J.
The convention of representing the sound /j/ as "y" is more familiar to English speakers. Since we are changing the spelling anyway when we transliterate from the Cyrillic alphabet, there's a tendency to use the option that makes it easier for English speakers to read the name with the right pronunciation. What German and Scandinavian languages do doesn't have much relevance in that context.
In fact, there are many ways to romanize Cyrillic and you could see /j/ represented as J or even I in some systems rather than Y. Y is just a popular way of doing it.
There are basically three ways to deal with foreign names in English text.
ك → k and ق → q in names of Arabic origin, even though English speakers will pronounce both as /k/.The transcription Юлия → Yulia results from option #2: Preserving the pronunciation /ˈjʉlʲɪjə/, or rather, its English approximation /ˈjuːli.ə/.
English orthography is famously phonetically ambiguous (e.g., a is pronounced /eɪ/, /æ/, /ɑː/, or /ə/ in different contexts), and thus it's not always obvious how to represent a sequence of sounds with letters (or vice-versa). But in general, English speakers have the expectation that j is pronounced /dʒ/, and y is pronounced /j/. And conversely, the expected spelling of /j/ is y, and not j. Hence, "Yulia".
Sure, some people may be aware of the fact that j is pronounced /j/ in German (or Polish, Dutch, etc). But that's irrelevant. English speakers will read "Julia" as /ˈdʒuːli.ə/. Even if you expect your readers to recognize the name as being different from the English "Julia", why expect them to pronounce J as German /j/ instead of as Spanish /x/~/h/, French /ʒ/, or Pinyin-Latinized Mandarin /tɕ/? We're translating from Russian into English here, so there's no point in introducing a spelling convention from some arbitrary third language.
In English, the letter “j” is (usually) /d͡ʒ/ and the fairly-common name “Julia” is pronounced /ˈd͡ʒuːli.ə/ even if the Julia in question is a historical figure that spoke Latin and would have pronounced the name /ˈi̯uː.li.a/ or /ˈju.li.a/ (depending on era, Classical vs. Ecclesiastical).
So for a modern person whose name is pronounced with the initial /j/ sound, “Julia” would be the wrong transliteration—“j” isn’t the (typical) letter that produces the /j/ sound in English. Instead, “y” (usually) does that. There are exceptions, typically from foreign names, but, those foreign names are 1. typically written in the Roman alphabet to begin with, so transliteration isn’t necessary, and 2. don’t have a conflict with an existing English name with a different pronunciation.
That said, Wikipedia lists at least a few notable figures with a /j/-initial “Julia” spelling.
The same names, e.g., of biblical or Roman origin, are often pronounced differently in various languages - in a manner more suitable to the phonetic rules of that language. Thus, Russian or Bulgarian name Yulia corresponds to English or French Julia, but not pronounced the same. Official transcription rules used, e.g., for latinizing Cyrillic script for passports, then would require that the name is spelled Yulia.
Another factor is that the same letter may correspond to different sounds: e.g., German Julia is pronounced as Yulia
As similar examples one could mention:
