Telling someone how to spell your name is probably pretty common in Japan, especially if your name has an uncommon spelling. Even just from watching anime, you see it happen pretty often. For instance, new students often write their name on the board (or the teacher does it for them), or during an introduction a character will say, "It's spelled with the Kanji for this and that." This prevalence in media leads me to believe it's a normal thing that happens.
If you know anything about Kanji, you know that you can't really tell how to pronounce a person's name just from reading the Kanji (of which there are thousands in common use, and even more than that not in common use). That's because Kanji have different readings, and there are even special readings for names. The reverse is also true. Just from the pronunciation, you can't necessarily tell how to spell it in Kanji, because multiple Kanji could be used. Unless you're using a pretty common spelling, you'd need to tell everyone that information.
In addition to just telling people, it seems business cards might also serve the purpose of conveying spelling and pronunciation. As per this article on Tofugu, the Japanese sometimes even carry around personal cards:
Business cards in Japan are called meishi 名刺, and are an important part of Japanese culture. Even outside of the business world, Japanese people sometimes have personal meishi made (meishi means "name card" after all).
In contrast, if the name is spelled in Katakana or Hiragana, you would likely know exactly how to spell/pronounce it just from hearing/reading it. That's because these two sets of symbols are a phonetic syllabary, as compared to the English language which has multiple pronunciations for the same letters.