Traveling to Italy in June for 8 days

I find it somewhat hurried, but it is doable.
Stay in Milan and have Lake Como as a day trip. After a possibly long flight, you don't want all the hassle of getting to Milan from the airport and then on to Lake Como. There are regular trains from Milan to different towns around Lake Como. Have a look at the website of the Italian railways for the connections on offer. (Use the Italian originals for place names. For Venice you want Venezia Santa Lucia; for Florence Firenze S.M. Novella.)
Don't have plans for Venice. Venice is for wandering around (and getting lost and finding your way again).
Pisa can easily be done as a day trip from Florence. Trenitalia website for connections.
Advance bought tickets for the longer journeys come with huge discounts if you don't mind being tied to a specific train. Process at the Trenitalia website is simple and reliable (credit card, emailed pdf for printing at home). Regionale trains don't come with discounts (they are cheap already) and have no reservation. Buy the tickets at the station. (I often do it the evening before to avoid a possible queue at the ticket window when my train is about to leave.)

When you consider the time spent checking out of a hotel, getting to the train station, the train ride itself, getting to a new hotel, checking in, and so forth, it always takes much longer than anticipated. And you don't have that much time in the first place. I'm afraid you'll have a lot of blurry memories of train stations. Personally I'd drop Lake Como. Yes, it's pretty, but the time lost getting there and back will not, in my opinion, justify the visit. I'd also drop Milan. Consider flying into Venice (one of the truly unique places in Italy), splitting your time between there and Florence, and then flying home from Florence. Do Pisa as a day trip from Florence if you really have to see it. Don't mean to rain on your parade, just food for thought.

Your planned itinerary is just a little aggressive for the time you've got. I'd suggest sticking to Milan, Florence and Venice.
Many on this forum like to fly open jaw into one city and out of another. It makes travel much more efficient than having to backtrack to your original arrival airport to depart.

For short trips, flying open jaw is critical - and probably cheaper. As recommended earlier, into Venice - 3 nights, 3 nights Florence with day trip to Pisa, and 1 night in Milan and home. Count your nights, not your days.

If I count correctly you have 7 nights on the ground. It's always best to count nights when you plan.
Remember that 2 nights in one place is only one full day on that place, plus a few hours the previous day when you arrive, which usually gets wasted in check-in procedures and getting orientied in the new city.

You don't say which airport in Milan you land. Intercontinental flights use Malpensa (MXP) which is a distance from the city (about 1 hr to the west). Most European flights arrive at Linate (LIN), the Milan city airport, which is near the city center (5 miles to the east of the city center). MXP to Lake Como will require at least 2+ hours by train (via Milan Centrale), therefore, after everything is said and done (deplane/bag claim/immigration/customs/train travels/etc), you won't get to Lake Como until the afternoon of your day of arrival. If you land at LIN it will be a bit faster, also because you will probably have done immigration already at your first port of entry in the EU.

At lake Como, I recommend to stay at Varenna, which is served by train service from Milan Centrale.
Two nights at Lake Como are good. That will give you a full day, after your arrival, to visit both Varenna and Bellagio, across the lake. Leave the visit of the city of Milan to the end of your trip. You will need to spend your last day in Milan since your flight home is the next morning.

After Lake Como, go to Venice. You need to take a train to Milan Centrale, then change to a fast train to Venice. The Varenna-Milan leg is a 70 min journey. The Milan-Venice leg is 2+ hours. So all included, from check out in Varenna to check in in Venice, it's probably close to 5 hours. Two nights in Venice are short, but that is all you can afford. That will give you at least a full day to enjoy Venice.

After Venice go to Florence by train (2h journey). Spend 2 days in Florence. That again gives you a full day in Florence. Short, but you can do something. Personally I would drop Pisa. Pisa can be visited in a couple of hours, but once you add the time to get there from Florence (1+ hr each way), at least half day is gone. You should not take away half day from Florence to visit Pisa IMO. If you had an extra night in Florence, then maybe, but not in your case.

So far we used 6 nights. You have one more (the night before the flight). That night must be spent in Milan. Leave from Florence early, take a frecciarossa to Milan (1h 40m journey) and you can have several hours to see Milan on your last day in Italy. The next morning head to the airport (by train if Malpensa, by taxi if Linate). Don't take the taxi to Malpensa. It costs a fortune (120 euro) and takes 45-60 min. Take the Malpensa Express train from the Cadorna Station (36 min). Possibly stay at a hotel near the Cadorna station, which is also walking distance from the Duomo, the Galleria, and the Last Supper.

You need to stay on top of the ticket situation for The Last Supper. Those sell very rapidly once they go on sale.

You will probably be sleep-deprived and jetlagged on your arrival day, so I think it's best to head somewhere that allows just wandering around outdoors and trying to adjust to your new time zone. For me, Venice would be ideal for that. Yes, flying into Venice would be best, but my reading of your post is that you've already bought round-trip tickets for Milan. So land in Milan and buy yourself a train ticket to Venice. Don't do it ahead of time, because you can't predict when you'll actually be ready to step on that train.

I agree that the schedule is a little much and would drop Lake Como if you really need that day in Milan.

I second Roberto's advice. Days 1 and 8 are pretty much lost to travel.

Thank you to everyone for your help. To answer an important question, I already purchased round-trip flights from Milan.

Do you think it would be better if we just kept our trip to Milan, Lake Como, and Venice with a brief stop in Verona? Would that make the trip more relaxed and less aggressive?

Again, I really appreciate you guys and this forum! Thank you so much!

Of course. Every time you change your bed you are losing at least a half day and sometimes more. Your proposal greatly reduces some of your travel times. What is your priority for what you want to see.

Two other nice cities right along that path are Padua (larger, or so it feels) and Vicenza. You could have a great vacation just moving along that railway line.

I think your revised plan is better in terms of less packing and moving around.