After a bit research I can not find anything about alternative names for quantum model of atom.
For Bohr's model 1, 2, 3... was used but it was for orbit not for orbitals.
According by According William B. Jensen Hund had followed Bohr’s practice of labelling the various shells and subshells in terms of their corresponding numerical
quantum numbers as $3_1$, $3_2$, $3_3$ etc.
But that was not followed(broadly speaking accepted) by other, So he replaced it by series notations (s, p, d, and f).
The reasons behind no alternative name according to me are:
The discovery is new compared to many discoveries which have different names during different time.
Modern Periodic Table was made during same period so they had to find something which can be used for years without changing it. So if they keep had change the name then most probably there should be change in modern periodic table(can't find any such reference).