Just do the rebranding, it's better to do it on the long run. Yes, it's a huge amount of work, but it could be done in a finite amount of time. The two names can co-exist, like
New name (formerly HxHxHx)
Furthermore not all name updates are equally important, some can be done with a DB find and replace some is shit manual work, but you can hire for this job someone.
Read about stories how companies did this before. Currently I can think of one case that's ongoing: Taxify -> Bolt. They still have the Taxify logo on their cabs in Hungary but the app updated to Bolt (taxify).
Read about stories how companies did this before. Currently I can think of one case that's ongoing: Taxify -> Bolt. They still have the Taxify logo on their cabs in Hungary but the app updated to Bolt (taxify).