Guys, is there a way to add a custom field to the syncing table e.g. with the name of my source? Like airbyte adds metadata fields such as _airbyte__ab_id, _airbyte__enitted_at, etc

No, today this is not possible @Igor. The most close issue related to this topic is: https://github.com/airbytehq/airbyte/issues/4025

@Marcos Marx (Airbyte) Thank you for your answer, will be looking forward to that feature