I couldn't find anything even remotely related in the documentation.
According to https://developer.atlassian.com/cloud/bitbucket/rest/api-group-repositories/#api-repositories-workspace-repo-slug-put
PUT https://api.bitbucket.org/2.0/repositories/{workspace}/{repo_slug} --data "{\"name\": \"${new_name}\"}"
Using the PUT method allows renaming of a repository.
According to https://confluence.atlassian.com/display/BITBUCKET/repository+Resource+1.0:
PUT https://api.bitbucket.org/1.0/repositories/{accountname}/{repo_slug} --data "name=new name"
This allows to update the visible name of a repository.