Update:
For private citizens using DHL they will require an EORI number. For businesses, they require a VAT (and possibly a EORI as well). I explained I was a US citizen with no VAT or EORI and DHL gave me two options.
Long Term Option:
Respond to an authorization email and DHL will apply for the EORI number for me as a private person. This will take a few extra days for the application to be granted, but does not cost me anything.
Alternative:
I can also have an updated invoice addressed to an Italian citizen who has an Italian Tax Code.
The updated invoice would be the faster option. I emailed DT responding to the emailed invoice that was sent to me to see if this is something we can do.
Thanks for reading!
Edit: I’m keeping the past information up so that others may be able to find it if they run into a similar problem. My problem however seems to be solved. After discussing my issue with my host company, it seems they should have this number stored for me and they registered it as part of my visa and residency. I should get this taken care of by the end of the day today 