Create searchable collection

Hi all
I am currently working on an app where people can showcase their collection of items. I’m looking for a best way for someone to find a specific user’s collection and profile?

I’d like the users to have a unique ID (of their choice if possible) that they could share with each other but it seems that this option is not available or complex to implement (I’ve read the solution with autoincremented counting).

Could someone explain me the best way to proceed for both collections and profiles (ultimately it’s easier to find a profile and from there look up the collection, I presume).
Thank you.

Could you have them search a list of users?

Yes, @Ben, I’d like to ideally them to search the list of users (preferably avoid searching by email address for privacy purposes) and then consult users public collection and profile (this would require 2 new screens probably on top of existing user profile screens?).
I’m just not sure how to best proceed for the search part (which data to search, full name, username which might not be unique etc.).
Thank you in advance.

it’s my personal opinion

I would search on full name.