Search for contacts on iCloud.com

You can search for a contact by name or any other information included on a contact card.

In Contacts on iCloud.com, click the list you want to search in the sidebar. If you want to search all contacts, select the All Contacts list.
Click Search [list name] at the top of the contacts list, then type the text you want to find. You can search for contacts by their name as well as by details, like phone number or address.
As you type the contact name or contact information into the search field, iCloud Contacts displays matching contacts with your search terms highlighted in each contact card.

To display your complete contacts list again, delete the text you entered in the search field.

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iCloud User Guide