10 Days for Greek Islands

You have a pretty rushed schedule. If you are flying in from the USA the first day will be a jet lagged blur. If you are flying from somewhere else in Europe I would try to get a direct flight to Santorini and save Athens for the end. Even if you have to come and go from Athens consider flying to Santorini instead of the long ferry ride. We each have our own travel styles, but 2-3 days on an island is a minimum for me.

Your plan has virtually no time in Athens aside from your arrival day--a day on which I am always non-functional. Athens is not a particularly charming city; it's not one where I'd want to hang out for weeks, just wandering around. But it has some very important archaeological sites and museums, and most people do want to see a few of them.

Only one day on Naxos is too little .

Just do santorini and Naxos .

Fly to santorini if you can as the ferry takes a long time from Athens .

Too much in too little time.

Athens deserves a minimum of two days with three being better. There's more to Athens than just the tourist sites.

Santorini is THE most popular and heavily touristed of the Greek Islands. October will give you some relief from the hordes of tourists but they'll still be the Cruise Ships spewing out hundreds if not thousands of tourists at a time. It's not my first choice for a Greek Island but to each their own.

Naxos is the largest of the Cyclades and deserves many days to fully experience one of Greece's best all-around islands.

Your schedule doesn't take into account the time involved from getting from one island to the other especially via a ferry. That will eat up a lot of time on a boat when you could be spending it on an island or Athens.

I would eliminate Paros and devote more time in Athens and/or Naxos.

I can't be a hypocrite about Athens, as I only gave it a day--but I tend to return to a place and I figured I'd be flying in there again to give it more time. If you just want to see the acropolis and get a good walk around in, a day is adequate.
I would carefully check the transit times--I think only two islands would be a much better use of your time. I would also try to get to the first island on the first day since you arrive early.

I can’t imagine not giving Athens more time. I would spend less time on overtouristed Santorini.

I’ve been to Athens once , many years ago , was crowded then , can’t imagine now .

I prefer the travel vibe on the islands, more laid back - with the exception of both Santorini and Mykonos which can be zoos .

A lot of this comes down to personal preference, neither is right or wrong

I’d adjust your schedule as follows:
Day 1 - arrive in Athens and fly directly to Santorini - 3 nights
Day 4 - Ferry to Naxos - 4 nights
Day 8 - Fly to Athens - 2 nights
Day 10 - fly home