The speaker says he talks to his dog in the same place he talks to the king, and the poem's small joke is that these two listeners are treated as equals. Both get the same privacy, the same lowered voice. The setting is "between home and bed," a tucked-away stretch of the day, which suggests the hour when the world's demands fall away and a person can speak plainly.
The title, "In/formal," fits well. The slash lets the word split into "informal" and "in formal," as if the speaker is both relaxed and a little ceremonial. Talking to a dog is casual; talking to a king is not. The poem blends the two without fuss.
The mood is calm, intimate, and gently humorous. The speaker seems content, even a bit tender. The short lines and the single-word line "privately" make the poem feel like a whisper, something shared only with the reader who has leaned in close.