How are block rewards claimed in merged mining? How do you claim a block reward on a merged chain?

If I understood it right: let's say you are mining Bitcoin and Namecoin. When you find the solution to a BTC block, you include a transaction in the block to give you a block reward.
If the hash of this block is also a solution for the Namecoin chain, where is the transaction giving you the Namecoin block reward? Where is the Namecoin address getting this reward? Or are Bitcoin addresses also valid Namecoin addresses?
And if you are only mining Bitcoin, can you claim the Namecoin block reward for a solved Bitcoin block afterwards?
The point of mining is to secure the blockchain. Before you mine, you must compose the block you are trying to find a nonce for. That block will include a transaction to pay you.

If you are merged mining Bitcoin and Namecoin, you do the following:

1) You compose the Namecoin block you are trying to find a nonce for. This includes a transaction to pay you the finder's fee.

2) You compose the Bitcoin block you are trying to find a nonce for. This includes a transaction to pay you the finder's fee and a transaction to secure the Namecoin block.

3) Now you try to find a nonce. If it meets the Bitcoin difficulty, you've mined a Bitcoin block. If it meets the Namecoin difficulty, you've mined a Namecoin block.

You submit a Bitcoin block the normal way. The information from the Namecoin block is ignored by the Bitcoin system.

You submit a Namecoin block along with enough information from the Bitcoin block and Merkle tree to prove that the nonce secures the Namecoin block.