The identification of political actors who put forward claims in public debate is a crucial step in the construction of discourse networks, which are helpful to analyze societal debates. Actor identification is, however, rather challenging: Often, the locally mentioned speaker of a claim is only a pronoun (“He proposed that [claim]”), so recovering the canonical actor name requires discourse understanding. We compare a traditional pipeline of dedicated NLP components (similar to those applied to the related task of coreference) with a LLM, which appears a good match for this generation task. Evaluating on a corpus of German actors in newspaper reports, we find surprisingly that the LLM performs worse. Further analysis reveals that the LLM is very good at identifying the right reference, but struggles to generate the correct canonical form. This points to an underlying issue in LLMs with controlling generated output. Indeed, a hybrid model combining the LLM with a classifier to normalize its output substantially outperforms both initial models.