Nuts. I hit this same error weeks ago, and after a lot of wasted time figured out how to make it work--but I've since forgotten it. (Not much help, other than to say yes, it can be done.)
Have you tried different combinations of brackets, or of with and without brackest? e.g.
EXEC sp_rename 'ENG_TEst.ENG_Test_A/C_TYPE', 'ENG_Test_AC_TYPE', 'COLUMN';
EXEC sp_rename '[ENG_TEst].[ENG_Test_A/C_TYPE]', 'ENG_Test_AC_TYPE', 'COLUMN';
EXEC sp_rename '[ENG_TEst].[ENG_Test_A/C_TYPE]', '[ENG_Test_AC_TYPE]', 'COLUMN';
EXEC sp_rename '[ENG_TEst].ENG_Test_A/C_TYPE', 'ENG_Test_AC_TYPE', 'COLUMN';
If all else fails, there's always
- Create new table (as "xENG_TEst") with proper names
- Copy data over from old table
- Drop old table
- Rename new table to final name