In [1]: import pandas as pd
   ...: import dask.dataframe as dd
   ...: import numpy as np
   ...:

In [2]: df = pd.DataFrame({
   ...:     'a': np.arange(20)**2,
   ...:     'ts': pd.date_range('01-01-2000', periods=20).map(str)
   ...: }, index=pd.Index(np.arange(20), name='id')
   ...:     )
   ...:

In [3]: ddf = dd.from_pandas(df, npartitions=4)

In [4]: ddf.index.name
Out[4]: 'id'

In [5]: ddf2 = ddf.assign(ts_parsed=ddf.ts.map_partitions(pd.to_datetime, meta='datetime64[ns]'))

In [6]: print(ddf2.index.name)
Out[6]:  None

.....

In [8]: meta = pd.Series([], dtype='datetime64[ns]')
   ...: meta.index.name = 'id'

In [9]: ddf2 = ddf.assign(ts_parsed=ddf.ts.map_partitions(pd.to_datetime, meta=meta))

In [10]: print(ddf2.index.name)
id