Language is a very versatile thing; and the meaning of words is a social convention, nothing more. So if two people agree in their conversation to call a ground-source heat pump geothermal, then it is, for them.
However, from what I've seen, it is more commonly the case that people call it geothermal as a mistake. Ground-source heat pumps are indeed solar energy collectors, unless you're somewhere like Iceland where the geothermal energy gives significant warming to the ground very close to the surface.
So yes, it is possible to have geothermal heat pumps. But almost all the cases I've seen where that name's been used, that's not what's going on. It's that someone's misunderstood where the heat has come from.
As a quick crude check, take the temperature of the area from where the heat will be extracted. at the depth it will be extracted. If that's about the same temperature as the year-round average surface temperature, then the heat has come from the sun. If it's more than 10 Kelvin (degrees Celsius) warmer than that, then it's geothermal.