Use isin
Df1.name.isin(Df2.IDs).astype(int)
0 1
1 1
2 0
3 0
Name: name, dtype: int32
Show result in data frame
Df1.assign(InDf2=Df1.name.isin(Df2.IDs).astype(int))
name InDf2
0 Marc 1
1 Jake 1
2 Sam 0
3 Brad 0
In a Series object
pd.Series(Df1.name.isin(Df2.IDs).values.astype(int), Df1.name.values)
Marc 1
Jake 1
Sam 0
Brad 0
dtype: int32