Hi @Sylvain_Ard
The easiest would be to generate a download based on a list of taxon names. We have some tutorials on how to do that here: Downloading occurrences from a long list of species in R and Python - GBIF Data Blog
Having all the data in one download will make citing the data much easier. See also our citation guidelines: https://www.gbif.org/citation-guidelines
Also check this thread about getting vernacular names: API Offset Limit - #3 by DG070