Buddha-nature is the point where Mahayana Buddhism comes closest to saying the thing it was founded to deny. The worry is not a Western imposition; the tradition raises it against itself.
The problem
Non-self (anatta) denies that any permanent, independent essence is found in a being. Emptiness (sunyata) denies that anything has an inherent, self-standing nature. Buddha-nature then says that all beings possess, or are, a luminous awakened nature, present from the start, obscured but never absent, needing only to be uncovered.
Read plainly, that is a permanent essence present in every being. Which is the atman, the Hindu self, under a Buddhist name.
The tradition's own answer
The Lankavatara Sutra puts the objection in the mouth of a questioner: if the tathagatagarbha is permanent and present in all beings, how does it differ from the self taught by the non-Buddhists? The sutra's answer is that buddha-nature is taught as skilful means, a teaching pitched to those who are frightened by the bare doctrine of emptiness and would recoil from it, drawing them in with positive language they can accept, and not to be grasped as a real, findable self. On this reading the positive words are a therapeutic device, and anyone who takes them for a metaphysical essence has made the very mistake the teaching was meant to prevent.
Why it stays unresolved
Not everyone accepts that the positive language is only provisional. The shentong view (set out under Sunyata) holds that buddha-nature really is empty only of what is extrinsic to it, and is not empty of its own luminous qualities, which is close to saying that there is, after all, something that positively exists at the ultimate level. Its opponents, the rangtong view, hold that buddha-nature is empty of inherent existence like everything else, and that the shentong position smuggles an essence back in.
So the question "is buddha-nature a self by another name?" has a tradition-internal answer, no, it is skilful means, and a tradition-internal dissent that will not let the answer settle. The atlas records the tension rather than resolving it, because the tradition has not resolved it either.