No, an object cannot be a black hole to one observer but not another. The concept of a black hole is an objective physical phenomenon with well-defined characteristics that are independent of the observer's perspective.
A black hole is formed when a massive object collapses under its own gravity, reaching a point of infinite density known as a singularity, surrounded by an event horizon from which nothing, including light, can escape. The presence of an event horizon is a defining characteristic of a black hole, and it is the same for all observers regardless of their location or motion.
The event horizon of a black hole represents a boundary beyond which no information or signals can reach an observer outside the black hole. Once an object crosses the event horizon, it is inevitably destined to be a part of the black hole's interior, known as the singularity.
While the perception of a black hole might differ for different observers due to relativistic effects like time dilation or gravitational lensing, the fundamental nature of the black hole remains the same. It is an extremely dense object with an event horizon that prevents anything from escaping its gravitational pull.
Therefore, whether an object is a black hole or not is an objective property of the object itself, and it does not depend on the observer's viewpoint.