We consider two scenarios of naming people in databases of news photos with captions: (i) finding faces of a single person, and (ii) assigning names to all faces. We combine an initial text-based step, that restricts the name assigned to a face to the set of names appearing in the caption, with a second step that analyzes visual features of faces. By searching for groups of highly similar faces that can be associated with a name, the results of purely text-based search can be greatly ameliorated. We improve a recent graph-based approach, in which nodes correspond to faces and edges connect highly similar faces. We introduce constraints when optimizing the objective function, and propose improvements in the low-level methods used to construct the graphs. Furthermore, we generalize the graph-based approach to face naming in the full data set. In this multi-person naming case the optimization quickly becomes computationally demanding, and we present an important speed-up using graph-flows to compute the optimal name assignments in documents. Generative models have previously been proposed to solve the multi-person naming task. We compare the generative and graph-based methods in both scenarios, and find significantly better performance using the graph-based methods in both cases.