How to shuffle column values while keeping same dataset

I would like to to shuffle some columns from a table in Postgres database. I have 2 millions rows. I need to update all not null values by another.

I need to keep the same dataset. It's not possible to have the same value two times. It's not possible to swap data with next values because, if I do the same process with another column I will keep the same link. It's to anonymise my database. Just need to shuffle data and keep the dataset.

exemple (change firstname and lastname):

id	firstname	lastname
1	albert	einsten
2	isaac	newton
3		curie
4	alexandre	Graham Bell
5	thomas	Edison

shuffle firstname column:

id	firstname	lastname
1	isaac	Graham Bell
2	albert	Edison
3		einsten
4	thomas	newton
5	alexandre	curie

How to do this with a speedy process?