No, that's a misconception started by people who don't know how to read kana.

Because of the way kana is constructed, you don't technically have "shu"; written down, you have "shyu." But you still pronounce it "shu" -- or, if it's at the end of a word, maybe just "sh."

"Mash" written in kana is "Masshyu," and if you didn't know you're supposed to ignore the Y (and downplay the U), that might look like it sounds like "Matthew." But it's really just Mash.