Yes, this is called "ghosting". Ghosting is when the ambient light exposure is close to the intensity level of the flash exposure. This happens at various times; it can be done deliberately, as a creative effect, most often when a person does what is called "dragging the shutter", which typically involves slowing the shutter speed wayyyyyy down in dimmer environments, so that there is plenty of ambient light that registers on the film or sensor, and the flash provides a crisp, flash-frozen image, which also has the ambient light recorded over a longer, slower time frame, which creates the ghost-type presence.
Ghosting can occur by accident in brighter areas; when there is a lot of light present, like in a bright place, the shutter speed that we're limited to with most cameras, like 1/250 or 1/200 or 1/160 second depending on camera model, means that if the lens aperture is sufficiently large in diameter, at that flash sync speed range, there is enough light to produce a ghost image, especially on things that are moving, or if the camera is not held rock-steady. In the shot with the ball, we can see the baby's hand is moving rapidly...and it also looks like the ball itself has a little bit of movement, which is what is giving the lettering on the ball that ever-so-slight second-set-of-lettering look.
If the ambient light exposure is significantly dimmer (darker, more-black) than the flash part of the exposure, by around 3 to 4 stops, then ghosting is usually not a problem. If however, the ambient exposure is close to what the light in the room needs to be exposed at, and a flash exposure is also used, ghosting can be pretty pronounced, as it is in this case.
I didn't look at EXIF info, but wanted to ask, is this automatic exposure, like in programmed mode? If the flash is being fired and the camera is using the flash as "fill light", then this is a pretty expected result. ADDENDUM: Since I began typing, I see you've added info RE your shutter speed, of 1/60 second, which is slowish. AND you shot this in "aperture priority", which most likely means that yes, the camera was striving for some kind of balanced fill-flash, and at 1/60 second with an ambient light exposure value, yeah, ghosting is going to be super-likely on moving subjects.