A Doppler shift at right angles to the line of sight is called what?

A Doppler shift at right angles to the line of sight is called the transverse Doppler effect.

“Transverse” means across or perpendicular to the line connecting the source and observer. In the classical treatment of waves, purely sideways motion might be expected to cause no frequency change because the source has no velocity component directly along the line of sight. Special relativity predicts a shift nevertheless.

The effect arises from time dilation and is therefore a specifically relativistic Doppler phenomenon. In a common formulation, the frequency factor for a perpendicular arrangement involves the Lorentz factor γ. The exact sign—redshift or blueshift—depends on the setup and on whether the angle is defined using the source’s apparent position, the point of closest approach, or the observer’s frame.

The Stark effect concerns spectral-line shifts caused by electric fields, Compton scattering involves photon–particle collisions, and the normal Zeeman effect is magnetic-field splitting of spectral lines. They are neighboring spectroscopy concepts, not names for a right-angle Doppler shift.