1. German origin: In German, it would be pronounced "Roo-ter" with a long "oo" sound similar to the "oo" in "moon."
2. English pronunciation: If the name is being used in an English-speaking context, it might be pronounced "Roo-ther" or "Rooth-er" with the stress on the first syllable.
3. Other possibilities: Depending on the individual and their background, there might be variations in pronunciation, like "Roo-thur" or "Ruh-ther".
Ultimately, the best way to know how to pronounce "Ruether" is to ask the person with that name how they prefer to pronounce it.