Variability characterization of tsunami generation is quintessential for proper hazard estimation. For this purpose we isolate the variability which stems solely from earthquake spatial source complexity, by simulating tsunami inundation in the near-field with a simplified digital elevation model, using nonlinear shallow water equations. For earthquake rupture, we prescribe slip to have a log-normal probability distribution function and von Kármán correlation between each subfault pair, which we assume decreases with increasing euclidean distance between them. From the generated near-field inundation time-series, emanating from several thousand synthetic slip realizations across a magnitude 9 earthquake, we extract several tsunami intensity measures at the coast. Results show that all considered tsunami intensity measures and potential energy variability increase with increasing spatial slip correlations. Finally, we show that larger spatial slip correlations produce higher tsunami intensity measure exceedance probabilities within the near-field, which highlights the need to quantify the uncertainty of earthquake spatial slip correlation.