So we have a DC level that, for example, varies between 0VDC and 10VDC in sinusoidal fashion. Is that classified as alternating current even though it does not go negative?
It's all a matter of perspective and relativity. What you have is really a 10V Pk-Pk AC level superimposed on a 5V DC level. So the answer is yes. But I agree the term alternating is muddy in this case.
However, when we remember that voltage is a relative term it makes more sense.
If we think of AC like the classic point on a wheel spinning round the sinusoidal AC part is easy to imagine. But if we extend that and mount that wheel on top of a moving trolley we get your scenario. If you are standing on the trolley you see the dot going backwards, if you stand on the ground, you don't.
The term "Modulation-Current" might be more appropriate..
Which brings up a another question...
Why do we say alternating current not alternating volts.. which is the units we are usually quoting? e.g 110V AC