This was long taken to be a self-portrait of Van Gogh and it is indeed similar to another self portrait of the same size. The brothers closely resembled one another, but research indicates that this must indeed be a portrait of Theo – the only one Van Gogh ever made of his 5-year-younger brother.
The man in this portrait does not have Vincent’s sideburns and his beard is more ochre-coloured than red. His shapely, round ear is also unlike Van Gogh’s, while matching that of his brother. The straw hat Theo is wearing looks more appropriate for Vincent, who is shown in the corresponding self portrait wearing a neat felt hat.
he brothers most likely swapped headgear for the occasion as a joke.
The portrait is unusually small and is painted in quite a lot of detail, suggesting that Van Gogh was trying to compete with portrait photos. He wrote some time earlier: ‘it’s a cause worth fighting... (https://www.vangoghmuseum.nl/en/collection/s0157V1962)
Added view: Vincent right; Theo left.