How to assign unique value based on two columns combinations in Python?

If you simply want a unique identifier for each combination of GENUS and SPECIES you can do the following:
Note: In have assumed that either GENUS or SPECIES can contain a None value, which complicates the process slightly.

So Given a DF of the form:

    GENUS   SPECIES
0   Murina  Coelodonta
1   Murina  Microtherium
2   Microtherium    Murina
3   Bachitherium    Microtherium
4   Coelodonta  None
5   Coelodonta  Coelodonta
6   Microtherium    Coelodonta
7   Microtherium    Murina
8   Microtherium    Bachitherium
9   Murina  Microtherium  

Add a column which uniquely identifies each combination of GENUS and SPECIES. We call this Column 'ID'.

Define a function to create a hash of entries, taking into account the possibility of a None entry.

def hashValues(g, s):
    if g == None:
        g = "None"
    if s == None:
        s = 'None'
    return hash(g + s)  

To add the column use the following:

df['ID'] = [hashValues(df['GENUS'].to_list()[i], df['SPECIES'].to_list()[i]) for i in range(df.shape[0])]  

which yields:

    GENUS           SPECIES         ID
0   Murina          Coelodonta      -6583287505830614713
1   Murina          Microtherium    6019734726691011903
2   Microtherium    Murina          -2318069015748475190
3   Bachitherium    Microtherium    5795352218934423262
4   Coelodonta      None            4851538573581845777
5   Coelodonta      Coelodonta      -5115794138222494493
6   Microtherium    Coelodonta      2603682196287415014
7   Microtherium    Murina          -2318069015748475190
8   Microtherium    Bachitherium    -2746445536675711990
9   Murina          Microtherium    6019734726691011903