Family names are usually straightforward (go with kun’yomi, unless the second character is 藤, in which case it’s on’yomi, and that’ll be correct about 90% of the time).
Given names, you’ll probably need to ask. Even native speakers aren’t always sure of the pronunciation of the name of a person they’ve never met before. It’s why business cards and official forms and such usually have furigana.
It’s not uncommon for teachers at my school to not remember how to read the given name of students. Most teachers have no reason to use the given name unless they are that student’s homeroom teacher or something.