I know it's in the title and the tag for this new artist was now created but maybe the title was a typo. Is the artist's name really supposed to be "Takanotume"?
It's definitely possible, look at page 24 for the author using that romanization for his Twitter account. Under several romanization systems つ is romanized as "tu." This is done in Kunrei-shiki romanization (訓令式ローマ字), which has some official legal status in Japan and is used for education. You will often find it used internally within Japan for Japanese people as well as with some foreign Japanese language learners. It also does し as "si" and ち as "ti" and so on. Since (in native words) the Japanese language always pronounces these mora the same way, for people familiar with Japanese it is easy to pronounce and it does respect the grammar better. In recent years there indeed have been attempts to borrow loan words with non-Japanese pronunciations, which is why such irregular kana like トゥ. Note however that If I just type "tu" in my Japanese input method on my computer I get つ not トゥ. Also note that for extremely common words like "smartphone," the pronunciation tends to assimilate to native Japanese, hence スマホ - "s(u)maho" is now more common than スマフォ "s(u)mafo." (English does the same thing when borrowing words and getting rid of diacritics.)
That said, some Japanese will switch between romanization systems even for a name, so if you'd like to try to verify it, feel free. But it's far from unusual for Japanese to use Kunrei-shiki, especially for something that is not being aimed at foreigners.
Saying that Japanese people should use a different romanization for つ than "tu" because it's not "really" that sound is akin to arguing that in English we should use different letters for the "t"s and "p"s in "top" and "pot" because the word-initial t in "top" is aspirated and the word-final t in "pot" is not, and same for the "p." (The "p" in "spin" is also not aspirated.) "But it's the same sound!" you say, and anyway when you're speaking English you always know how to say it, and it never distinguishes one word from another (there is no word also spelled "top" but pronounced with an unaspirated t that means something different). In other words, it's "allophonic" in English.
Well, guess what? Those consonants are distinguished in almost all variants of Chinese, as well as in Korean. So what's "the same" to English ears is different to other ears, just like with Japanese.