A picture of a long object (let‘s say your long rod) can be taken this way: you place a row of photo cameras along the rod and make clicks by these photo cameras simultaneously in your frame. Then you glue all these pictures into one.
This way, yes, different observers (photographers) moving with different velocities relatively to a measuring rod, would see different set of events. or different, not identical to each other rods. If the rod is covered with clocks, all these clocks will show different time, i.e. every infinitesimal part of it would appear to be of different age. So. if in the rest frame of the rod it starts rusting from the both ends simultaneously, in some other relatively moving frame it will appear almost untouched from one and almost completely rusted to the middle from the other end.
If there are many identical brothers at some distance apart from each others, let‘s say 30 years old in their rest frame, from the other relatively moving frame some of them may appear still sucking a pacifier while some others lying in a coffin already.
Obviously it is because of Einstein synchronization in each frame of reference.
To get rid of this rubbish all moving observers must choose another synchronization. They must take one arbitrary frame (that could be the frame of the rod) and take into account their velocity relatively to this frame and synchronize their clocks (clicks of photo cameras) accordingly. Obviously in these frames one way speed of light will not be c.
Imagine, that the rod rusts from the both ends in its rest frame simultaneously and disappears due to rusting. If you will describe remainder of the rod perfectly well, you will get its velocity.
That means, an abstract rod has ANY velocity. Even in Special Relativity a well – defined (or described) (remainder of the) rod has EXACT velocity, since there is one and only one frame, from which this exact remainder of the rod can be seen.
By the way: Feynman talking about definitions of objects - http://www.feynmanlectures.caltech.edu/I_12.html, about a chair, starting from: - Any simple idea is approximate; as an illustration, consider an object ...