  Under two different metric ansatzes, the noncommutative geometry inspired
black holes (NCBH) in the framework of Rastall gravity are derived and
analyzed. We consider the fluid-type matter with the Gaussian-distribution
smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown
that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in
Rastall gravity, unlike its counterpart in general relativity (GR), is not a
regular black hole. It has at most one event horizon. After showing a finite
maximal temperature, the black hole will leave behind a point-like massive
remnant at zero temperature. Considering a more general metric ansatz and a
special equation of state of the matter, we also find a regular NCBH in Rastall
gravity, which has a similar geometric structure and temperature to that of
NCSBH in GR.
