ENH: When chaining multiple .merge() functions, only the second "suffixes" param produces results
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python

df =pd.DataFrame({'year':[2005, 2006], 'cusip':['111', '222']})
df_comp = pd.DataFrame({'year':[2005, 2006], 'cusip':['111', '222'], 'test': [5, 10]})

df_comp['year'] = df_comp['year'].astype(int)
df = df.merge(df_comp, how='left', on=['cusip', 'year'], indicator=True, suffixes=[None, '_wyear'])
print(df['_merge'].value_counts())
df = df.drop(columns='_merge')

df_comp2 = df_comp.drop(columns='year').drop_duplicates()
df = df.merge(df_comp2, how='left', on=['cusip'], indicator=True, suffixes=[None, '_woyear'])
print(df['_merge'].value_counts())
df = df.drop(columns='_merge')

print(df.columns)

```
Index(['year', 'cusip', 'test', 'test_woyear'], dtype='object')

#### Problem description

The suffixes parameter of _merge only produces a suffix for the second merge not the first. This behavior persists if I switch the two merges. 

#### Expected Output

Index(['year', 'cusip', 'test_wyear', 'test_woyear'], dtype='object')

#### Output of ``pd.show_versions()``

<details>
C:\Users\Hiwi_Tower\AppData\Local\Programs\Python\Python38\python.exe "W:/Lehrstuhlverzeichnis/300_Forschung/310_Aktuelle_Projekte/Paper Hauke/Python/Digital/getdigitalanalysts.py"

INSTALLED VERSIONS
------------------
commit           : 2cb96529396d93b46abab7bbc73a208e708c642e
python           : 3.8.0.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19041
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : de_DE.UTF-8

pandas           : 1.2.4
numpy            : 1.18.1
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 20.2.4
setuptools       : 41.2.0
Cython           : 0.29.14
pytest           : 6.2.3
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : 1.2.7
lxml.etree       : 4.5.0
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : 4.8.2
bottleneck       : None
fsspec           : 2021.04.0
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.1
numexpr          : None
odfpy            : None
openpyxl         : 3.0.3
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.3
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : None
numba            : None

</details>
