Opening Madness


1.e4 d5 is the Scandinavian, a completely different opening to the Italian. It's OK to have the Italian as your main choice for white but you don't get to decide what black is doing. If you are going to play 1.e4 you need to have a little basic knowledge of the following:
1.e4 e5 2.Nf3 Nc6 you are happy because you can play Italian.
but...
1.e4 e5 2.Nf3 Nf6 Petrov
1.e4 c5 Sicilian
1.e4 e6 French
1.e4 d5 Scandinavian
1.e4 c6 Caro Kann
1.e4 d6 Modern/Pirc
And slightly less common...
1.e4 Nf6 Alekhine
1.e4 b6 Owen
You cannot play against all these other main openings in the same way that you play your favourite Italian game. The plans and ideas are completely different.

And trying to recall what the dubious 1.e4 e5 2.Nf3 d5 is called (Elephant gambit) I found this game where Emil Diemer defeated 'Stutterer' using it 😆 Whoever he was I'm sure he would have preferred NN to this!

It's not necessary or even a good idea to go into great detail on all this stuff, there is so much information that you will drown in it. Perhaps search YouTube for beginner level introductions for these openings just to get an idea about them. You haven't played many games here...what level are you at? If you are right at the start of your chess journey I would even probably say that it's best to ignore this stuff for now. Just get your pieces developed in the opening and focus on trying not to lose material throughout the game. These opening details are not so important until you can play games without making catastrophic blunders. But just be aware that if you play the same way against everything you will run into problems. A simple example...1.e4 e6 2.Bc4 you try to play in the style of Italian vs a French defence but black goes d5 and it is clear that your bishop does not belong on c4.

another approach is to study beginner opening theory, rather than all these specific lines.
simple stuff, really: control the center: d4,d5,e4,e5 are the pure center, c4/c5 and f4/f5 are sort of the extended center, control what you can of them. Move knights out to f/c positions usually. move your bishops somewhere sensible. castle. Move your queen somewhere safe and productive. Avoid moving the same thing a bunch of times. Capture towards the center with pawns usually. There are videos and articles and all that explain these basic ideas in more detail.
the opposite of this is zerk out with your queen and attack stuff right away, or lead with your rook pawns and pull your rook out first thing, or other random things that serve no purpose.

I know the first few moves of the mainlines of only a few openings. Opening principles is fine up to at least 1500 if not beyond. You will pick stuff up as you go and get better at playing opening principles.
The trick is to spend the time you would have used learning openings to instead work on tactics, calculation, positional chess and middlegame ideas. Then you can outplay your opponents as soon as they go off book.

The Italian Game is comprised of the following three major openings/variations...
Giuoco Pianissimo - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d3
Giuoco Piano - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4
Two Knights Defence - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6
Succinct overviews of the Italian Game - the primary variations, and their themes and plans...
https://simplifychess.com/italian-game/
for more on openings, check out...
Chess Openings Resources for Beginners and Beyond...
https://www.chess.com/blog/RussBell/openings-resources-for-beginners-and-beyond
https://www.chess.com/blog/RussBell
In the opening every move has a reason. In most positions there are several moves that have a good reasoning behind them, sometimes there are only a few good moves. Even the so called system openings (King's Indian Attack, London system, Colle system, ...), in which you can play the same moves against most setups, cannot be played without thinking against any setup.
The Italian is not a system opening, so you will definitely have to adjust your play to what your opponent does. You can still use the idea of "natural development", which means starting with central pawn(s), then developing the knight(s), developing the bishop, castling - given that your opponent has not created any threats meanwhile. If possible you should of course create threats yourself. With time you will get familiar with the main ideas in the common openings (there are lessons here and you can use the opening explorer to see, what master level players play in each position).