Publishing through an Occurrence Core you could put the synonyms in previousIdentifications (https://dwc.tdwg.org/terms/#dwc:previousIdentifications), but even better in terms of richness would be to include an Identification History extension (https://tools.gbif.org/dwca-validator/extension.do?id=dwc:Identification). That would allow you to capture richer information about the names, if desired, but more importantly, one per row in the extension, and multiple rows per Occurrence, if necessary. fyi @teleaslamellatus
Publishing through an Occurrence Core you could put the synonyms in previousIdentifications (https://dwc.tdwg.org/terms/#dwc:previousIdentifications), but even better in terms of richness would be to include an Identification History extension (https://tools.gbif.org/dwca-validator/extension.do?id=dwc:Identification). That would allow you to capture richer information about the names, if desired, but more importantly, one per row in the extension, and multiple rows per Occurrence, if necessary. fyi @teleaslamellatus