ALTER FUNCTION changes the definition of a function. The only functionality is to rename the function.
The name (optionally schema-qualified) of an existing function.
The data type of an argument of the function.
The new name of the function.
To rename the function sqrt for type integer to square_root:
ALTER FUNCTION sqrt(integer) RENAME TO square_root;
There is an ALTER FUNCTION statement in the SQL standard, but it does not provide the option to rename the function.