When we are storing parent and child records in single salesforce create call using PHP toolkit is it required the External_ID_Field__c same name in both objects? or we can use any field which is carrying same value in both object

Like in my case I have two objects one is contact(parent) and another is course_c(this is custom child object) in both object I have one field in contact(Postgres_ID__c) and in another object course_c(Contact_ID__c) which content same id data.

So Can I use this fields while storing the data in Parent child records as a external_id_field_c.

Thanks in advance.