No. The data is analyzed with $\nu_1, \nu_2,\nu_3 $, well defined by their mixing matrices in the PDG, but, before the resolution of the hierarchy, they cannot be identified firmly with the classroom poster placeholder names $\nu_L, \nu_M,\nu_H $, Lightest, Middle, Heaviest.
In the normal hierarchy, the two sets identify ordinally; ultimately, after the resolution of the hierarchy, somebody will think of good names--but not as good as my linked answer's: Huey, Dewey, and Ratatouille, needless to say...
The PDG poster above is a vast advance w.r.t. the older version of that poster featuring the oxymoronic weak-charged-current "eigen"states $\nu_e,\nu_\mu,\nu_\tau$, regrettably still featured in dark corners of WP, and often referred to as "lepton flavor eigenstates", an absurd and confusing name indicating lepton flavor is thereby ipso facto violated!!
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