Hi and
Its a Cholla. You should transplant it CAREFULLY.
Are you putting it into another pot? Or the ground? If in a pot, the pot its in is large enough - leaving it there is safer than transplanting to another pot. Approach this plant cautiously - the spines have little barbs that go in quite easily but don't come out again. Visualize a cactus covered in porcupine quills.
Daisy