In the documentation there is a field in the cohort_definition table called cohort_instantiation_date: https://github.com/OHDSI/CommonDataModel/blob/master/Documentation/CommonDataModel_Wiki_Files/StandardizedVocabularies/COHORT_DEFINITION.md
In the ddl this field is called cohort_initiation_date: https://github.com/OHDSI/CommonDataModel/blob/master/Sql%20Server/OMOP%20CDM%20ddl%20-%20SQL%20Server.sql#L175
I don't think anyone has used this field ever. I suggest sticking to cohort_initiation_date and changing the documentation so we don't have to update all our databases and software.