In the umbrella concept forgefriends wouldn’t need to be renamed. It is the umbrella for a collection of “forge friend” initiatives. But the technical implementation (the FOSS project creating forge proxies) would have to be renamed. For instance along more of a ‘end-user perspective’, be something like “Forgefriends ProjectBridge” or whatever. And then you’d have “ProjectBridge for Gitea”, “ProjectBridge for Gitlab”, etc. The renaming would be for repo names, and changes to code to reflect that.
ForgeFed, being a spec, may become “Forgefriends Federation Protocol v1.0” and have sections for “Issue management”, “Merge requests”, etc. Or you could break those down into seperate document artifacts “Forgefriends Issue Management v1.0”.
(You might name apps along the domain of metal working e.g. IssueWelder, CodeMold, SparkReview, etc … can create some great mascotte avatars for that 
See: Glossary of Blacksmithing and Metalworking Terms - English)