Dimensionality plays an essential role in determining the nature and properties of a physical system. This is particularly evident in quantum systems, where interactions and fluctuations are enhanced in lower dimensions, leading to various different quantum effects. Here we show that strongly interacting ultracold bosons perceive their dimensionality as either one or two, depending on whether they are probed on short or long distances, respectively. We probe this dimensional crossover using a thorough analysis of the momentum distribution to study the characteristic decay of the one-body correlation function in the two dimensionalities and track how the decay is modified during the crossover. We find a varying two-slope structure, which substantiates the main result. These observations demonstrate how quantum properties in the strongly correlated regime evolve in the dimensional crossover as a result of the interplay between dimensionality, interactions and temperature.