There are many ways one might implement a circular buffer, that's not really important. The point is that you should use the standard names, so people may easily compare your "Double-ended vector" to the state of the art.
Inserting 4 into:
[x, x, x, 1, 2, 3]
Produces: [4, x, x, 1, 2, 3]
In a circular buffer, and: [x, 1, 2, 3, 4, x]
In the proposed "double-ended vector". The technique is different, the amortized complexity is also different. I think therefore, it warrants a different name, to avoid confusion.