The observation and simulation of the variability of coastal sea level are impacted by various uncertainties, such as measurement errors and sampling biases, unresolved processes, and model and forcing biases. Ocean model simulations suggest that another uncertainty should be taken into account for the attribution of sea-level changes. Global ocean simulations indeed show that resolving mesoscale turbulence (even partly) promotes the emergence of low-frequency (LF) chaotic intrinsic variability (CIV) which causes substantial random fluctuations of sea level up to multiple decades in eddy-active regions of the world ocean. This random LFCIV is superimposed on the atmospherically forced (or simply "forced") fluctuations, which are directly controlled by the atmospheric variability. We show from a large ensemble of global oceanic hindcasts that this multi-decadal LFCIV leaves a substantial imprint on the long-term trends (1993-2015) of coastal sea level: over 17-20% of the global ocean coastal area, in particular along the coastlines of the northwestern Pacific and Indian Oceans, and around the Gulf of Mexico, random sealevel trends may blur their atmospherically forced counterpart, such that simulated (and potentially observed) coastal sea-level trends cannot be unambiguously attributed to atmospheric or anthropic causes. The steric and manometric sea-level change contributions of these uncertainties are discussed, suggesting that they mostly come from the manometric sea-level trends near the coasts.