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After the commands you gave, you can "rename" the generators:

sage: e12
PBW[alpha[2]]
sage: e12.rename('e12')
sage: e12
e12

After the commands you gave, you can "rename" the generators:

sage: e12
PBW[alpha[2]]
sage: e12.rename('e12')
sage: e12
e12

I don't know of an automated procedure, but maybe you could modify pbw_basis (and hence PoincareBirkhoffWittBasis) to take an extra argument to give names to the generators.