Oracle:

ALTER DATABASE LINK

ALTER DATABASE LINK dblink
{ CONNECT TO user IDENTIFIED BY password [ dblink_authentication ]
| dblink_authentication
};

dblink_authentication::=
AUTHENTICATED BY user IDENTIFIED BY password

example

ALTER DATABASE LINK private_link
CONNECT TO hr IDENTIFIED BY hr_new_password;

ALTER PUBLIC DATABASE LINK public_link
CONNECT TO scott IDENTIFIED BY scott_new_password;

ALTER SHARED PUBLIC DATABASE LINK shared_pub_link
CONNECT TO scott IDENTIFIED BY scott_new_password
AUTHENTICATED BY hr IDENTIFIED BY hr_new_password;

ALTER SHARED DATABASE LINK shared_pub_link
CONNECT TO scott IDENTIFIED BY scott_new_password;