Hi Stefan,
When you say "checkout API" are you talking about cart permalinks (http://www.shopify.ca/technology/4849802-new-feature-cart-permalinks)?
If so, you can pass the company field as so: http://store.shopify.com/cart/70881412:1,70881382:1?billing_address[company]=example+company
Let me know if I misunderstood your question
- Christian