Two experiments were carried out to examine the effects of dominant right versus non-dominant left exploration hand and left versus right object orientation on haptic recognition of familiar objects. In experiment 1, participants named 48 familiar objects in two blocks. There was no dominant-hand advantage to naming objects haptically and there was no interaction between exploration hand and object orientation. Furthermore, priming of naming was not reduced by changes of either object orientation or exploration hand. To test whether these results were attributable to a failure to encode object orientation and exploration hand, experiment 2 replicated experiment 1 except that the unexpected task in the second block was to decide whether either exploration hand or object orientation had changed relative to the initial naming block. Performance on both tasks was above chance, demonstrating that this information had been encoded into long-term haptic representations following the initial block of naming. Thus when identifying familiar objects, the haptic processing system can achieve object constancy efficiently across hand changes and object-orientation changes, although this information is often stored even when it is task-irrelevant.