Your pre-planning is a MOST refreshing change from far too many who seem to never plan ahead, hope for the best, and then become frustrated (or worse) when things don't work as they'd assumed.
Your intentions were indeed understood on all counts; but thanks for clearly double-confirming.
Changing a SIM should not change your device's "trustworthiness."
It only changes your phone number.
That said, you WILL need to update your phone's "reachable at" (in your phone's AppleID settings) if you want your friends and associated to reach you via iMessages and/or FaceTime using your Italian phone number.
I'd suggest experimenting with another SIM here in the U.S. prior to departure. The cost of a cheap prepaid SIM is trivial relative to experience and piece of mind it should provide pre-travel. (more on this further down)
Now ... At the risk of changing subjects on you yet again ...
You might consider changing your current stateside primary carrier to an e-SIM if they offer it. (Assuming that you're using an iPhone Xs/Xr or newer)
This would allow you to keep your US number active w/o any changes upon arrival in Rome (although you can turn it off) ... and then install and shift to the Italian "physical" SIM for Primary Voice and Data.
It moves the "learning curve" stateside BEFORE departure, and allows you to thoroughly test and become familiar w/the steps before travel (which inevitably brings it's own stressors)
Using Dual SIM is not particularly difficult, but it's not something I'd want to attempt for the 1st time in a foreign country.
Using Dual SIM with an eSIM - Apple Support
Alternatively, you could keep your US "hard" SIM and install an Italian eSIM; however I'd never recommend this to anyone eSIM'ing 1st time; some experience should be acquired - preferably in one's native language - beforehand.
