Dogamy is the pair card to Dogaressa. He has the same attack and defence stats as his wife but reversed. If he is placed on the field after Dogaressa his Magic will activate. However this will not activate if placed before Dogaressa. Likewise her Magic will not activate if placed before Dogamy.
It is recommended if you do have both cards in your deck to place this one first as it will likely last longer, unless you're going for a more aggressive playstyle or wish to attract attention and kill a card by using the higher attack stat of Dogaressa. Particularly useful en masse in the Integrity and dog Decks.