Public Contact Info

I wanted to create a public contact card so when my clients click a button on my website it traverses them through the iMessage API and instantly adds a contact card with photo and name as a background task. If there is implications my next question was going to be if there is a possible way to create a public contact card where for example I could redirect a client to iMessage and when starting a new conversation if they type in a name it pops up instead of needing to utilize a phone number? I am trying to explain my thought process as much as possible but I have been typing for hours. In simple terms is there a possibility to create a public contact card that can be accessed or texted by anyone who types in a name into new conversation bar?

Public Contact Info
 
 
Q