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We discuss the properties of Hα emission stars across the sample of 22035 spectra from the Gaia-ESO Survey internal data release, observed with the GIRAFFE instrument and largely belonging to stars in young open clusters. Automated fits using two independent Gaussian profiles and a third component that accounts for the nebular emission allow us to discern distinct morphological types of Hα line profiles with the introduction of a simplified classification scheme. All in all, we find 3765 stars with intrinsic emission and sort their spectra into eight distinct morphological categories: single–component emission, emission blend, sharp emission peaks, double emission, P-Cygni, inverted P-Cygni, self–absorption, and emission in absorption. We have more than one observation for 1430 stars in our sample, thus allowing a quantitative discussion of the degree of variability of Hα emission profiles, which is expected for young, active objects. We present a catalogue of stars with properties of their Hα emission line profiles, morphological classification, analysis of variability with time and the supplementary information from the SIMBAD, VizieR, and ADS databases. The records in SIMBAD indicate the presence of Hα emission for roughly 25% of all stars in our catalogue, while at least 305 of them have already been more thoroughly investigated according to the references in ADS. The most frequently identified morphological categories in our sample of spectra are emission blend (23%), emission in absorption (22%), and self–absorption (16%). Objects with repeated observations demonstrate that our classification into discrete categories is generally stable through time, but categories P-Cygni and self–absorption seem less stable, which is the consequence of discrete classification rules, as well as of the fundamental change in profile shape. Such records of emission stars can be valuable for automatic pipelines in large surveys, where it may prove very useful for pinpointing outliers when calculating general stellar properties and elemental abundances. They can be used in studies of star formation processes, interacting binaries, and other fields of stellar physics