Pandas: filling missing values by mean in each group

One way would be to use transform:

>>> df
  name  value
0    A      1
1    A    NaN
2    B    NaN
3    B      2
4    B      3
5    B      1
6    C      3
7    C    NaN
8    C      3
>>> df["value"] = df.groupby("name").transform(lambda x: x.fillna(x.mean()))
>>> df
  name  value
0    A      1
1    A      1
2    B      2
3    B      2
4    B      3
5    B      1
6    C      3
7    C      3
8    C      3

fillna + groupby + transform + mean

This seems intuitive:

df['value'] = df['value'].fillna(df.groupby('name')['value'].transform('mean'))

The groupby + transform syntax maps the groupwise mean to the index of the original dataframe. This is roughly equivalent to @DSM's solution, but avoids the need to define an anonymous lambda function.