Suitable terminology for the inverse elasticity?
Economists generally call it the "inverse elasticity". But note
$$\frac{1}{\eta}=\left(\frac{\partial Q}{\partial P}\frac{P}{Q}\right)^{-1}=\frac{1}{\left(\frac{\text{% change in quantity}}{\text{% change in price}}\right)}=\frac{\text{% change in price}}{\text{% change in quantity}}$$

Thus, whilst the price elasticity of demand can be interpreted as (roughly)


  The percentage change in quantity sold that would follow a one percentage point increase in the price.


the inverse elasticity (the "demand elasticity of price") could be explained as


  The percentage change in price necessary to achieve a one percentage point increase in quantity.