PostgreSQL 8.0.1 Documentation
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ALTER FUNCTION

Name

ALTER FUNCTION -- change the definition of a function

ALTER FUNCTION name ( [ type [, ...] ] ) RENAME TO newnameALTER FUNCTION name ( [ type [, ...] ] ) OWNER TO newowner

ALTER FUNCTION changes the definition of a function.

name: The name (optionally schema-qualified) of an existing function.
type: The data type of an argument of the function.
newname: The new name of the function.
newowner: The new owner of the function. To change the owner of a function, you must be a superuser. Note that if the function is marked SECURITY DEFINER, it will subsequently execute as the new owner.

To rename the function sqrt for type integer to square_root:

ALTER FUNCTION sqrt(integer) RENAME TO square_root;

To change the owner of the function sqrt for type integer to joe:

ALTER FUNCTION sqrt(integer) OWNER TO joe;

There is an ALTER FUNCTION statement in the SQL standard, but it does not provide the option to rename the function or change the owner.