To be specific, we have different lineages of E. coli. I wondered if the ortholog genes among them should all have the same name in all lineages or can they also have different names?
Gene naming is pretty subjective and even a single gene can have many names. If you're lucky orthologs will be named the same in different lineages, but you can't rely on it. Better to use gene ids (e.g. from Ensembl) and an ortholog db to map the orthologs. However, if you're looking at different strains, this is more tricky since most db don't go below the species level