I'm a Software Architect who looking for a corresponding term for position and dimensions of an object at the sametime.
Is there a word or term for that in geometry or analytic geometry?
No, there is no such term. Dimensionality would depend on the frame of reference and the attitude/orientation of the object. Is dimensionality taken with respect to the object, or to the reference frame?
In general, in mathematical modeling you can associate with an object of interest a concept known as a state space. This is simply a set of variables that describe properties of the object, e.g. mass, acceleration, position, rotation, and so forth. Most of the time, physical spatial dimensionality is not considered for rigid objects, because those dimensions don't change with respect to the object; however, for things like morphing structures, these do change, and are considered in the state space representation.