Yes, it would be best if you always inform the client as to why you’re closing their ticket. Even if it’s only to say, “The issue you reported has just been resolved, so we’re closing your ticket”.
If you’re putting a ticket on pause, it’s even more important to let the customer know. Each time a ticket is put on hold, you have to communicate it to the client, explain why it’s happening, and inform them how long it will take to resolve the matter or even how long it will take to reopen the ticket. Otherwise, clients may feel forgotten or uninformed, and this kind of situation won’t provide an outstanding customer experience for them.