Zero’s answer is basically a reduce operation. If I had more than a handful of dataframes, I’d put them in a list like this (generated via list comprehensions or loops or whatnot):
dfs = [df0, df1, df2, ..., dfN]
Assuming they have a common column, like name in your example, I’d do the following:
import functools as ft
df_final = ft.reduce(lambda left, right: pd.merge(left, right, on='name'), dfs)
That way, your code should work with whatever number of dataframes you want to merge.