ECC public key encryption and authentication - ECIES with ECDSA vs ECDH with AES
ECDH or DH for that matter doesn't provide any authentication of a user. ECDSA as a public key scheme does provide authentication, but lacks validation. You need to certify that the exchanged public keys are indeed from Alice or Bob. So Alice and Bob must let an authority certify their own public keys such that Alice trusts the authority of Bob and Bob trusts the authority of Alice. The authorities might in fact be the same authority. You can call it certificate authority.

A possible attack might be a man-in-the-middle attack where


Alice sends $K_A$ to Bob, but Martin intercepts $K_A$ and sends a newly generated key $K_{MA}$ to Bob
Bob sends back his public key and a signature, containing both public keys and her identity: $K_B,Sig_B(K_B,K_A,A)$, but Martin intercepts it and sends a newly generated key $K_{MB}$ and re-signs with its private key $Sig_{MB}(K_{MB},K_A,A)$
Alice replies similarly with her signature: $Sig_A(K_A,K_B,B)$, but Martin intercepts it and re-signs $Sig_{MA}(K_{MA},K_B,B)$ with the private key $MA$ from #1.


This is applicable to ECDH and ECDSA.