I'm using the latest version on Android.
I talked to Olga, and tried renaming them before meeting Gabby and Cath. I can rename the following:
Jack's First and Last Name.
Hiro
Shiki
Maria and Jack's personas
Raven's porn name and brand
Jack's bar
Grace's blog and gym
The flowers
Erik's Island
Jenn's and Jack's porn accounts
Jenn's restaurant
Rachel and Jack's pet names.