I might need some clarification on the question. Do you mean the name entered for the point in the editor doesn't have a hyphen and designation? Or does the official website of each of these features not include a hyphen and designation?
As long as the name you enter for the point matches the name listed on an official/authoritative source (e.g., the website run by the school) then you don't have anything to worry about. If the official name includes a hyphen, then that can be included in the name you enter for a point. If the official name does not include a hyphen, then you do not need to enter one. Or, if a school has multiple campuses, then a hyphen can be used in the name to separate the school name from the campus name: e.g., "Brown High School - Denver Campus".Campus".
A designation such as High School, Middle School, School, etc., should always be included in the name though. I recommend reviewing the [Name and Address Formatting Guide](https://navigator.er.usgs.gov/help/WebHelp/tnmcorps_attribute_formatting.pdf "Name and Address Formatting Guide").