How to efficiently assign unique ID to individuals with multiple entries based on name in very large df

I'd like to take a dataset with a bunch of different unique individuals, each with multiple entries, and assign each individual a unique id for all of their entries. Here's an example of the df:

      FirstName LastName  id
0     Tom       Jones     1
1     Tom       Jones     1
2     David     Smith     1
3     Alex      Thompson  1
4     Alex      Thompson  1

So, basically I want all entries for Tom Jones to have id=1, all entries for David Smith to have id=2, all entries for Alex Thompson to have id=3, and so on.

So I already have one solution, which is a dead simple python loop iterating two values (One for id, one for index) and assigning the individual an id based on whether they match the previous individual:

x = 1
i = 1

while i < len(df_test):
    if (df_test.LastName[i] == df_test.LastName[i-1]) & 
    (df_test.FirstName[i] == df_test.FirstName[i-1]):
        df_test.loc[i, 'id'] = x
        i = i+1
    else:
        x = x+1
        df_test.loc[i, 'id'] = x
        i = i+1

The problem I'm running into is that the DataFrame has about 9 million entries, so with that loop it would have taken a huge amount of time to run. Can anyone think of a more efficient way to do this? I've been looking at groupby and multiindexing as potential solutions, but haven't quite found the right solution yet.