Is it better to call the doppler effect a change in wavelength or frequency?

The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer.

In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in frequency. So it's a matter of relativity. To the traveling observer (in the source), only the wavelength is changing, to the stationary observer (experiencing the doppler shift) both frequency and wavelength have changed.

^{Lookang, Wikimedia commons. More simulations and applets here.}