The concept of time stopping at the event horizon of a black hole is a popular notion based on general relativity, but it can be misleading when taken too literally. In reality, it is more accurate to say that time appears to slow down for an outside observer as an object approaches the event horizon, due to the extreme gravitational effects near the black hole.
When we talk about black holes merging, we are referring to the process in which two black holes come close to each other and eventually combine to form a single, more massive black hole. This phenomenon has been observed indirectly through gravitational wave detections by instruments like the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo detector.
During a black hole merger, the event horizons of the individual black holes play a crucial role. As the black holes get closer, their event horizons overlap and then merge together. However, the idea that time stops at the event horizon does not prevent this process from occurring. It is a description of the extreme gravitational effects near the event horizon, but it does not imply a complete cessation of all physical processes.
For distant observers, the merging process would appear to take a finite amount of time, although it may appear to be significantly slowed down due to the gravitational time dilation caused by the strong gravity near the black holes.
It's important to note that a detailed understanding of the physics at and inside the event horizon of a black hole requires a theory that unifies general relativity with quantum mechanics, such as a theory of quantum gravity. While there are ongoing efforts to develop such a theory, our current understanding is limited to classical general relativity for describing the behavior of black holes.