We are adding the Vendors in Square but now we need to know the vendor when retrieving the Orders with the API. We can’t see the Vendor name in the order, item or item_variation, is there any way to get it or even the Vendor id? Or how are we supposed to know exactly what item was sold without the Vendor coming up in the API?
With the orders that are returned with the API the order will have the catalog object IDs as the line items. You can then use those ID to call the Catalog API to get the specific item details of that order. Unfortunately, the vendor_id isn’t in the orders nor at this time is there a way to get all the catalog objects for a specific vendor with our APIs. Your database would need to manage what items are associated to each vendor in Square at this time. We’re constantly working to improve our features based on feedback like this, so I’ll be sure to share your request to the API product team. 
About use the catalog object ID, do you mean we can ge the Vendor that way? Because we just tried to do it and the response includes the item variations and it’s price but we don’t see anything about the Vendor?
About getting all the items for a specific Vendor, we don’t need to get all the catalog objects for a specific vendor, we just need the Vendor of the sold item. Can it be done somehow?
About managing the Vendors in Square, yes we have it updated but we need a way to know what Vendor item was sold when we get the Order details while retrieving the Order. How can we do it?
Unfortunately no, at this time you can’t get the vendor from an order nor at this time you can’t get the vendor from the catalog item. We’re constantly working to improve our features based on feedback like this, so I’ll be sure to share your request to the API product team.