If you have the ability to make multiple requests, then:
- there is such a method
https://1b.app/ru/api/get-user-by-phone/ but it allows you to search only by phone number
- there is such a method
https://1b.app/ru/api/users/ where you need to use "Parameters for getting one contact", and in the request parameters you need to specify one of the parameters
In any case, you need to first check the phone, then check the mail or vice versa, and only then create a contact using /api/contact-add/json/
As for the name, this is not a unique parameter, although you can try to specify the name, namelast or contactNamefull parameters, but they are not declared as working (but it can work), although even if it works, then by the name of Sergey, you can get 20 contacts and which one them to choose a difficult question