No, the fact that your host already has a folder called "admin" does not matter. I have numerous sites running on hosts that have an "admin" folder and it makes no difference when you rename as long as you set your paths in the config file correctly (make sure you have included all the trailing slashes, and you do not need to actually reference the file in the url ... just the path to the directories will do).
The process is:
1) Rename the admin folder
2) Change the proper lines in the admin config file.
3) Change the proper lines in the catalog config file.





