There may be other names for it but for Buddhists this is the doctrine of 'dependent existence' or 'dependent origination'. This states that everything that exists (or seems to) does so in dependence on other existents thus does so only relatively. Thus existence is not fundamental but emergent.
It is a common view. The principle is famously proved by Nagarjuna in his Fundamental Verses on the Middle Way, also by Bradley in his Appearance and Reality and by GS Brown in Laws of Form.
It is not a subjective as opposed to objective view but takes us beyond the subjective/objective distinction.
It would be the reason why one thing alone cannot exist. At least two things would have to exist for one thing to exist and these two need an environment, which is three things. Monism fails where it implies that the world reduces to one existing substance or thing. It succeeds where it reduces existence to a phenomenon beyond substances, things, number and quantity thus beyond form.
It is the idea of dependent existence that makes sense of the mystical or non-dualist claim that nothing really exists. Where it does exist it would be only dependently or relatively, thus nothing exists independently or fundamentally.
The generic name for this philosophy would be 'non-dualism'. It may also appear as monism of a subtle kind. 'Advaita' (not-two) is a well-used name that conveys the idea. It may also be called 'mysticism' or the 'Perennial' philosophy. It is the only view that does not run into conceptual problems with piles of turtles or eternally-existing atoms.
It may also be called 'relative phenomenalism'. This phrase seems to have come into use with an article for the Journal of Consciousness Studies by Edward Barkin. Here's an extract.
"The idea behind modern phenomenalism would be that neither the transcendental object or subject exists in any concrete sense. Instead, one would postulate various possible combinations of phenomenal objects, the most coherent, complex and structured of which could be viewable as constituting emergent conceptual minds such as our own. In this case, the universe could be seen as fundamentally rooted in phenomena or mind.
As a result, there would be a tendency to reify mental phenomena, as in Berkeleian objective substance monism. However, I would argue that to do so would be as much of a mistake as to reify physical entities, since even the most basic mental properties can be shown to have a conceptual, and hence relative, non-objective aspect. In this idea’s original context, mainstream Buddhist philosophy, one would say that the reason to avoid endowing anything, including a qualitative state or a self, with the property of intrinsic, independent reality is that no object can be logically established without implicit or explicit reference to the causes and conditions which enable it to exist - including its parts and attributes and the very fact that a consciousness is required to mentally designate it a distinct entity in the first place. This principle is known as ‘dependent origination’ or ‘the interdependent nature of reality’. “
JCS Vol 10 No. 8 (2003)