Names such as Hilary and the like? (5)
I believe the answer is:
terms
'names' is the definition.
(terming is a kind of naming)
'hilary and the like?' is the wordplay.
'hilary' becomes 'term' (Hilary term is a term at the University of Oxford).
'and the like?' becomes 's' (I can't justify this - if you can you should believe this answer much more).
'term'+'s'='TERMS'
'such as' acts as a link.
Can you help me to learn more?
(Other definitions for terms that I've seen before include "Stipulations, often joined to conditions" , "Academic periods" , "Parts of the academic year" , "Times" , "Conditions (contract)" .)