The moniker, "Zelkova nire" seems to be unique to bonsai culture and not the name of the species. ThePlantList.org lists the following names for the genus (I have highlighted the names that are accepted at this point:
Name Status Confidence level Source Date supplied
Zelkova abelicea (Lam.) Boiss. Accepted M WCSP (in review) 2012-03-26
Zelkova acuminata Planch. Synonym L TRO 2012-04-18
Zelkova carpinifolia (Pall.) K. Koch Accepted M TRO 2012-04-18
Zelkova crenata Spach Unresolved L WCSP (in review) 2012-03-26
Zelkova cretica (Sm.) Spach Synonym M WCSP (in review) 2012-03-26
Zelkova davidiana (Priemer) Bean Synonym M TRO 2012-04-18
Zelkova davidii (Hance) Hemsl. Synonym M TRO 2012-04-18
Zelkova formosana Hayata Synonym L TRO 2012-04-18
Zelkova hirta C.K. Schneid. Synonym L TRO 2012-04-18
Zelkova hyrcana Grossh. & Jarm. Synonym M TRO 2012-04-18
Zelkova japonica Dippel Unresolved L WCSP (in review) 2012-03-26
Zelkova japonica var. verschaffeltii Dippel Synonym L WCSP (in review) 2012-03-26
Zelkova keaki Maxim. Synonym L TRO 2012-04-18
Zelkova schneideriana Hand.-Mazz. Accepted M TRO 2012-04-18
Zelkova serrata Makino Unresolved L TRO 2012-04-18
Zelkova serrata (Thunb.) Makino Accepted L TRO 2012-04-18
Zelkova serrata var. tarokoensis (Hayata) H.L. Li Synonym L TRO 2012-04-18
Zelkova sicula Di Pasq., Garfi & Quézel Accepted M WCSP (in review) 2012-03-26
Zelkova sinica C.K. Schneid. Accepted M TRO 2012-04-18
Zelkova stipulacea Franch. & Sav. Unresolved L WCSP (in review) 2012-03-26
Zelkova tarokoensis Hayata Synonym L TRO 2012-04-18
Zelkova ulmoides C.K.Schneid. Unresolved L WCSP (in review) 2012-03-26
Zelkova × verschaffeltii (Dippel) G.Nicholson [Unplaced] Unresolved L WCSP (in review) 2012-03-26