Both the contacts and companies records doesn't store the logo on a property and currently there isn't a way to retrieve the logo via HubSpot API. However, you can learn more about how to change or remove object record's logo on this article: Change or remove a record's image.
companies API: what is the field name for the logo?
Any update on this @WendyGoh? We're currently looking at manually adding multiple thousands of company logos (one by one) to a separate database and merging with other data from the Hubspot API to get around the blocker of having no endpoint to the logos stored on our entries in Hubspot.