How are block rewards claimed in merged mining?
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.