I went ahead with workflow since its easy to implement then trigger, here are the step by step, hope this will help others too:
At first let us create a new Field on the custom object/standard object.
1. Go to Setup | Customize | Accounts | Fields.
2. Scroll down to Custom Fields & Relationships Section.
3. Click New Field.
4. Select the Type as: Text
5. Name it as: Account Name Dupe Check[Field_Name_Dupe_Check, 255].
6. Check the Option: Unique and also select: 'Treat "ABC" and "abc" as different values (case sensitive)'.
7. Make it Visible for the appropriate Profiles. While you make them Visible also check the Option: 'Read Only'.
8. You need not put them on the Page Layouts.
Now, let us create a new Workflow Rule[Account Dupe Check].
1. Go to Setup | Create | Workflows & Approvals | Workflow Rules.
2. Click New Rule.
3. Select the Object: custom or standard object
4. Evaluation Criteria: created and every time it's edited.
5. Rule Criteria: criteria are met.
6. Field: select your field OPERATOR: not equal to
7. Save & Next.
8. From under Immediate Actions, click Add Workflow Action to select 'Field Update'[Set the Name].
9. Select the Field to Update: object Name Dupe Check
10. Select: Use a formula to set the new value
11. In the formula box, type in 'Name'.
12. Click Save.
13. Click Done.
14. Activate the WFR.