Well, as it said. I think that it means you can't have white space when you save a entity name.
Just like if I type _aaa (_ means white space) it appears:
Name is a required field and uniquely identifies the property, service, or event within the entity you are editing. You cannot include spaces, special characters (you can use hyphens and underscores), or leading numbers (you can use numbers within or at the end of the name). Names are case-sensitive.
Hope this solves your question.
I have seen this happen with copy and paste before. Sometimes whitespace characters get included in the copy and when pasted, they don't appear to be there, but still are when saving. Not sure if you are copying and pasting into the field or not, but in case you haven't tried already - make sure you actually type in the name.
Since this appears to be such a simple problem, but is more than likely not, maybe a screenshot would help us help you better?