What is it called when an object accelerates sideways?
I assume you mean by this acceleration in a direction perpendicular to the direction of the velocity.
This is called centripetal acceleration.
Or perhaps angular acceleration?
For cars it's called lateral (cornering) acceration for the component of acceleration perpendicular and sideways to the direction traveled, and longitudinal acceleration for the component of acceleration in the direction traveled. Vertical acceleration is used for the accerlation perpendicular and upwards / downwards to the direction traveled, (dips, rises, suspension reactions). Most high end race cars and even some computer racing games include full telemetry that captures all of this data in real time, allowing a driver / car engineer / player to analyze the results afterwards. Even some club racers will use telemetry boxes, like this one that also includes a pretty shift indicator as in this souped up porcshe at Road America:
Automotive Engineering (AE) uses the term fore-and-aft acceleration for the component of accerlation in the direction traveled. So this terminology isn't consistent.
Separate names with a comma.