> The little contact icon that shows up offering my entire contact book info
First off, I've never seen Safari offer all my contacts. That hints to me that you haven't defined your card in Contacts (effectively that means Safari doesn't know who you are.
If that's the case, you can open Contacts.app, find your contact card, and use the Card -> Make This My Card menu
Secondly, even with that card defined, there are two parts to how Safari identifies which fields to auto-fill.
The first, preferred path, is that the web page includes hints on the form fields, identifying which fields relate to which data (name, credit card number, expiry date, etc.). This is considered a HTML standard, and is controlled by the web designer and is nothing you can affect (other than reaching out to the web site telling them to get with the times.
For reference, check: https://html.spec.whatwg.org/multipage/form-control-infrastructure.html#autofill
Since not everyone follows the standard, each browser also uses heuristics to try and predict what the fields relate to - for example, it might assume a field called 'Name' would relate to the user's name. Confusion abounds, though, when field names are not consistent (e.g. different designers may differentiate between 'Name', 'FirstName', 'First_Name', and the browser has to make a guess as to which one to use).
