I think I chose the wrong road bike size
Almost all road bikes have your torso leaning forward to some degree, meaning you have to hold your head up constantly. If you've never ridden a true road bike before, you've probably never had to do that. What's the longest ride you've done on a road bike before this two-hour ride?

Since you didn't mention your hands or arms hurting, you're probably not leaning too far forward.  Leaning forward (to get lower and more aerodynamic) can put more weight on your hands and can make your hands, arms, and/or shoulders hurt or go numb after a while, especially if you're not used to doing that.

But since you rode for 2 hours before things started hurting, your bicycle's size probably isn't too far from being correct.

So your sore neck is probably just from doing something for two hours that you're not used to.  There's a good chance you just need to ride more and get used to holding your head up.

As you ride more, you may find other fit issues.  You may have to get a completely different saddle, and it might take you three or four different attempts before you find a saddle you can ride without discomfort after some period of time.  You may find your shoes and/or pedal combination starts making your feet hurt or gives you hot spots (you'll know what a "hot spot" is and why it's called that if/when you get one....).  You may find certain brands of shorts have padding that rubs your nether regions raw.  As already noted, you might have your hands go numb after a while.  Welcome to cycling - that's all a part of it.

But it's important to note that you apparently had NONE of those issues in a two-hour ride, and you seemingly haven't ridden your new road bike for that long ever before.  So you're really doing pretty well, and in my opinion you probably don't have to change much, unless you've left something out of your question.

At least not yet...