If your dog is registered with ANIS, you will receive a confirmation letter from them with your account and pin numbers. (My recent mutt was registered on 3 January, I just received the confirmation letter today, FWIW.)
If you don't have this letter, call ANIS ( www.anis.ch
) give them the chip number, and ask the status of your dog's registration. They are very helpful folks and will advise you what to do next.
It would be odd that the transport company did the ANIS registration - first time registration is supposed to be done by a vet. But who knows, we've seen all sorts...
If in doubt, if you have further problems, see your vet, he/she will take care of the bureaucracy for you. (Cost of ANIS registration is 20-40, usually rolled into an initial consultation visit - total usually under 100.) You'll want to get to know a vet anyway, an introductory visit is always recommended.
Don't stress about the 10 day thing - just follow up on the registration both, ANIS and at the Gemeinde/Polizei. And make sure you understand which training classes (federal, cantonal) you are required to do.
And enjoy your Swiss adventure - always more fun shared with a four footed friend!
If you don't yet have a passport, your vet will give you one. There is a new format from 1 Jan 2015, do make sure you get the new version.