Japanese names can be confusing, even for the Japanese, because the same kanji can have different meanings and pronunciations.
That's why you'll often see a Japanese name have a version of hiragana next to it.
Ex. 謙 (ゆずる)
That Kanji could mean Ken, Yuzuru, Kenshuu, Kenshou, Kenji, Kensou or Nori. But the hiragana explains that it's Yuzuru.
For Syuri or Shuri it's the same as Syu or Shu for Shu Shibutani.
Their names are write with digraphs, which are sort of like conjunctions. These are done by using smaller versions of Ya, Yu & Yo. (や, ゆ, よ)
So Shuri's name is written in Hiragana しゅり.
し = Shi
ゅ = Yu
り = Ri
But the small Yu make it a conjunction with the Shi, so it's pronounced "Shyu." It can be written Syu or Shu but I was taught that it's Shu.
So also しゃ = Sha & しょ = Sho.
For Takako, there's no hiragana for "co" in Japanese, so that's either stylistic or it wasn't available for her blog.
According to her Japanese wikipedia page her name in hiragana is たかこ.
た = Ta
か = Ka
こ = Ko