He also has at least one other companion, a friendly character who appears at regular intervals in different clothing. Piranesi holds this Other in high esteem - he is trying to understand the House but is unwilling to spend much time there, or travel far. On occasion the Other brings him gifts - new shoes for instance.
To the reader there is some clear overlap with our own world. The Other's gifts and outfits for instance. Piranesi also seems to have some knowledge of a time and place before the House, which helps him invent an explanation for what the House is. But the reader learns at the same time as Piranesi what is happening and what the House is.
The story is very compelling - I finished it almost in a single setting, as I rushed to the end to work out what was going on. The ending is remarkable and quite shocking, though Clarke gradually allows the real world to break through into the House (and Piranesi's) reality. Highly enjoyable, I think this will repay repeated readings.