How To Create A Covering Index

I have a table there is a query which has bad performance. This query normally can not use index because a lot of 'IS NULL','OR','LIKE' USED in where clause. I want to create a covering index for this query so it can use index scan only rather than Processor had to look up the row columns it needs
from a table or a clustered index.

current there are two index apply on that table:

CREATE UNIQUE CLUSTERED INDEX [Person_RecordID_UIX] ON Person
(
[RecordID] ASC
)
go

ALTER TABLE [Person] ADD CONSTRAINT Person_PK PRIMARY KEY NONCLUSTERED
(
[EntityID] ASC
)



How to add a covering index for the columns such as familyName,givenName, dob. All of these columns are not too much high selective.
Can I do like the following :

--create third index

CREATE NONCLUSTERED INDEX [Person_Cover_IX] ON [dbo].[Person]
(
[EntityID] ASC
)
INCLUDE ( [FamName],

[FirstName],

[DOB],

[Gender]
)

Or DROP Current index on entityid and recreate it with include clause.

What's the different between these two.

Thank you.