Is there a General Nurse designation between LVN and RN?

No, there is no such thing as a General Nurse designation between LVN and RN. The two nursing designations are Licensed Vocational Nurse (LVN) and Registered Nurse (RN). LVNs are licensed to practice nursing under the supervision of a physician or RN. RNs are licensed to practice nursing independently and can supervise LVNs.