Jeya's point is true, but the example doesn't really make sense. You would not normally use either word in that situation. Licensed is the word to use there.

To designate is to give a name to. So - an animal can be designated the official animal of a country. A track could be designated a national 'great walk'. To appoint is to assign a position to - as in a job, or a role. So - a team can appoint a leader, a club can appoint an auditor. With 'honorary positions' - you could use either word, although appoint would usually be most common.

I think appoint works best with people, not things. Whereas designate works equally well with both. e.g The KFC franchise is exclusively designated to sell the KFC food. The KFC franchise is exclusively appointed to sell the KFC food. Here I would say appointed does not work..