Sorting out all the correct names for the Opuntias is going to be a huge undertaking as the botanical world does not really seem to have come to a uniform nomenclature - yes there are the official lists, but the moment one starts looking in detail at what those lists are based on it becomes apparent that for Opuntias a lot remains to be determined/resolved. On Opuntiads.com, this plant is presented separately as O. gomei - with the spineless version given the cultivar name 'Old Mexico'. The authors of that website state that it has been conflated with O. lindheimeri, which itself is not recognized by all taxonomists as a separate species - it is often given as a variety/subspecies of O. engelmannii, which to me is very distinct from O. lindheimeri.
Given it is pretty distinctive appearance, it would not be bad to give it a separate entry with it name and synonym, but maybe stating that it represents a currently unresolved species.