As there is no direct extension in Amazon Connect , the agent Login Name is used as caller ID for outbound calls where the other party will always get the phone number defined in Amazon Connect as Caller ID.
Example
Agent Login Name is TomEvans. Outbound caller ID assigned to this user is +4975255184000 (typically it is the main office number or a hotline number).
In Salesforce, the Caller ID shown is TomEvans and also this ID is saved in the call task while the other party sees +4975255184000 as caller ID.