I believe that a constant velocity moving object in empty space within it own frame of reference retains its rest mass as long as it is moving at constant velocity and an effective mass increase occurs due to inertia only during acceleration.
But of course I could be wrong?
Within its own reference frame, the object itself has zero velocity. Thus, it has to retain its own rest mass at all times in its frame.
In fact, that's how rest mass is defined. It is the mass measured in the frame of the object.
Anything in its own reference frame views itself as being at rest so will always measure its rest mass only. when you view it from a different reference frame where you see the object has a velocity and you can apply the Lorentz transform for mass under special relativity
$$m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$$
to determine its relativistic mass and from there app;y $E=mc^2$ to find the energy of the particle.
