Remembering Thụy Sĩ is the Vietnamese name for Switzerland I did a quick search and turns out the name means Spring Water, possibly also gentle woman.
So, opening my dusty dictionary I was able to find Thùy means "lobe". Couldn't finy any Thúy, though.
all of Thúy, Thủy, Thùy and Thụy are Vietnamese name, the first 3 are usually used as girl's name. Thúy means beautiful or nice, Thủy means water and anything belongs to it, Thùy has many meanings, but I believe it means gentle. I don't know what does Thụy means but maybe it's similar to Thụy hiệu or Posthumous name, maybe it means that hope to always be remembered.
Thùy that you found in the dictionary and the name have the same way to speak and write but they are different words have different meanings, I don't know how to call it in English but in our language they are called: Từ đồng âm.
Most of Vietnamese names are Sino-Vietnamese words, their meanings and the way to pronounce come from ancient Chinese, and some of them are so hard to understand