Situation is:
Currently, I have a repository name phimpme-iOS. I want to capitalize the first letter of the repository, Phimpme-iOS.
User names and repository names are case-insensitive at Github: phimpme-iOS is the same as Phimpme-iOS; that is, from Github PoV you're trying to rename the repo to an equivalent name.
Try a completely different name — xxx, for example — and then rename it once more to Phimpme-iOS.
Rename your repository to something completely different (e.g. "foo") and then name it back to the original name with the desired capitalization.