In author name disambiguation, author forenames are used to decide which name instances are disambiguated together and how much they are likely to refer to the same author. Despite such a crucial role of forenames, their effect on the performances of heuristic (string matching) and algorithmic disambiguation is not well understood. This study assesses the contributions of forenames in author name disambiguation using multiple labeled datasets under varying ratios and lengths of full forenames, reflecting real-world scenarios in which an author is represented by forename variants (synonym) and some authors share the same forenames (homonym). Results show that increasing the ratios of full forenames improves substantially the performances of both heuristic and machine-learning-based disambiguation. Performance gains by algorithmic disambiguation are pronounced when many forenames are initialized or homonym is prevalent. As the ratios of full forenames increase, however, they become marginal compared to the performances by string matching. Using a small portion of forename strings does not reduce much the performances of both heuristic and algorithmic disambiguation compared to using full-length strings. These findings provide practical suggestions such as restoring initialized forenames into a full-string format via record linkage for improved disambiguation performances.