Index For Username/password

Does this make sense for a logon table:

CREATE TABLE Logon
(
ID INT NOT NULL IDENTITY PRIMARY KEY,
name VARCHAR(15) NOT NULL,
password VARCHAR(15) NOT NULL
)
GO
CREATE UNIQUE INDEX IX_Logon_Name ON Logon(name)
CREATE INDEX IX_Logon_NameAndPassword ON Logon(name,password)
GO

I do want the name to be unique but also will search frequently on both
name & password. Is this how it should be done? I don't fully
understand the difference between placing a single index in name &
password VS one on both name & password.