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.

You could try this if you have 3 dataframes

# Merge multiple dataframes
df1 = pd.DataFrame(np.array([
    ['a', 5, 9],
    ['b', 4, 61],
    ['c', 24, 9]]),
    columns=['name', 'attr11', 'attr12'])
df2 = pd.DataFrame(np.array([
    ['a', 5, 19],
    ['b', 14, 16],
    ['c', 4, 9]]),
    columns=['name', 'attr21', 'attr22'])
df3 = pd.DataFrame(np.array([
    ['a', 15, 49],
    ['b', 4, 36],
    ['c', 14, 9]]),
    columns=['name', 'attr31', 'attr32'])

pd.merge(pd.merge(df1,df2,on='name'),df3,on='name')

alternatively, as mentioned by cwharland

df1.merge(df2,on='name').merge(df3,on='name')

This is an ideal situation for the join method

The join method is built exactly for these types of situations. You can join any number of DataFrames together with it. The calling DataFrame joins with the index of the collection of passed DataFrames. To work with multiple DataFrames, you must put the joining columns in the index.

The code would look something like this:

filenames = ['fn1', 'fn2', 'fn3', 'fn4',....]
dfs = [pd.read_csv(filename, index_col=index_col) for filename in filenames)]
dfs[0].join(dfs[1:])

With @zero's data, you could do this:

df1 = pd.DataFrame(np.array([
    ['a', 5, 9],
    ['b', 4, 61],
    ['c', 24, 9]]),
    columns=['name', 'attr11', 'attr12'])
df2 = pd.DataFrame(np.array([
    ['a', 5, 19],
    ['b', 14, 16],
    ['c', 4, 9]]),
    columns=['name', 'attr21', 'attr22'])
df3 = pd.DataFrame(np.array([
    ['a', 15, 49],
    ['b', 4, 36],
    ['c', 14, 9]]),
    columns=['name', 'attr31', 'attr32'])

dfs = [df1, df2, df3]
dfs = [df.set_index('name') for df in dfs]
dfs[0].join(dfs[1:])

     attr11 attr12 attr21 attr22 attr31 attr32
name                                          
a         5      9      5     19     15     49
b         4     61     14     16      4     36
c        24      9      4      9     14      9

This can also be done as follows for a list of dataframes df_list:

df = df_list[0]
for df_ in df_list[1:]:
    df = df.merge(df_, on='join_col_name')

or if the dataframes are in a generator object (e.g. to reduce memory consumption):

df = next(df_list)
for df_ in df_list:
    df = df.merge(df_, on='join_col_name')