My inclination is to leave them alone until May or June. By then the foliage will be of help in identifying.

Relocating at this time and having late freezes hit could do harm. Are your freezes over?

Pictures would be helpful. Possibly neighbors have seen them in bloom? Another idea is to dig up one and take to a knowledgeable plant person. Or perhaps replant that portion in full sun.

When I had Siberian I don't recall them looking like long potatoes sticking out of the ground. Potato makes me think of beardeds' rhizomes. Tho they tend to be horizontal.

Sounds like bearded iris to me. First they need a sunny location with excellent drainage; digging in extra sand would not hurt them at all. The large sword shaped fan of leaves can be cut back if they look tattered but leave the smaller leaves intact as they will grow larger in the coming months. Make sure you plant them with the top 1/3 of the rhizome (thickened root) exposed to sunlight otherwise you will get no flowers. If any part of the root is mushy or damaged cut it off with a sharp knife (like slicing a potato!)before planting. Water well to begin and then only when very dry for a long period of time(over 2 weeks).