However, in the cases of wind, solar, and geothermal, this isn't so
obvious -- nothing is being used up (at least not in a measurable
quantity) which would need to be renewed.
Furthermore, there's no need to manage wind, solar, and geothermal
energy -- it isn't possible, on human scales, to overuse these.
For wind and solar there isn't a "store" that is being used up and replenished - instead the energy flux from the sun is being diverted. Wind power removes some of the kinetic energy from the atmosphere. This energy comes from the sun as heat, and after being converted to electricity and "used" will end up as heat, so the net result is the same, with some of the conversion being done in human appliances rather than atmospheric turbulence. The scale of what we divert is tiny in comparison with the global energy flux, but as others have noted the human-induced changes can be seen in local areas, and if we were to scale wind up enough might be noticeable globally.
Solar is more direct: There is a certain amount of sunlight falling on a given area of the planet. Normally it will be converted to heat, but with a photovoltaic panel in the way a fraction of it will be converted to electricity instead, and will then later be converted to heat (by an electrical appliance).
Geothermal is different, and at human scales may or may not be renewable, depending on the rate at which heat is extracted compared to the rate at which it is replaced from underground heat sources. These heat sources may simply be adjacent hot rocks (in which case only a low rate of extraction can be replaced) or it may be that you're Iceland and you're extracting from a volcano, in which case you're not going to make a dent in the thermal energy just beneath ;-)
Being strictly correct, geothermal power is not renewable at a planetary, long-term, scale, because the Earth is cooling and geothermal energy extraction hastens that cooling by a tiny fraction, but that hardly matters for human purposes.
Note that ground source heat pumps and the like, commonly advertised as "geothermal", are not usually operating off the internal heat of the planet, but instead are working in the top few metres that has been warmed by the sun - so they are arguably a form of solar energy. In this case there is a "reservoir", which is the heat energy in the soil, which is replenished by the sun, and it's conceivable that in densely populated areas an overuse of heat pumps could temporarily deplete this reservoir.