I always go the route of converting any identifier to the most stable ID that there is, which is Ensembl gene ID. Then I use these gene IDs (via biomaRt) to get an ortholog table, and with these orthologs I continue. From the ortholog gene IDs you can then go back to more readable gene names for the species at hand. For convenience I always use geneName_geneID as identifiers, so you have it all combined in a single string and the human-readable gene name is just a regex away (for plotting etc). Same goes for the GMT. Convert it to IDs first, then go along with this. Between species, a given gene either will have one ortholog, or multiple or none, so the length of the genes per GMT entry will almost certainly change.