Rivers that cease to flow are globally prevalent. Although many epithets have been used for these rivers, a consensus on terminology has not yet been reached. Doing so would facilitate a marked increase in interdisciplinary interest as well as critical need for clear regulations. Here we reviewed literature from Web of Science database searches of 12 epithets to learn (Objective 1—O1) if epithet topics are consistent across Web of Science categories using latent Dirichlet allocation topic modeling. We also analyzed publication rates and topics over time to (O2) assess changes in epithet use. We compiled literature definitions to (O3) identify how epithets have been delineated and, lastly, suggest universal terms and definitions. We found a lack of consensus in epithet use between and among various fields. We also found that epithet usage has changed over time, as research focus has shifted from description to modeling. We conclude that multiple epithets are redundant. We offer specific definitions for three epithets (non-perennial, intermittent, and ephemeral) to guide consensus on epithet use. Limiting the number of epithets used in non-perennial river research can facilitate more effective communication among research fields and provide clear guidelines for writing regulatory documents.