SharePoint BCS connectivity - Change Column name

We have a list created through BCS using external content type from SQL Database table. During creation, few columns were created as dummy(dummy 1, dummy 2 etc.) in SQL table which have replicated to the SharePoint list as well. Now the SharePoint list columns look like below

column 1,

column 2,

dummy 1,

dummy 2 .. etc.

Now, there is a business requirement to update the dummy 1 column to say 'column 3'. Now, where should I start my work?--

Should I update the Database table with correct column name initially and will it flow to SharePoint column automatically.

or

Should I update the Database with correct column name and then do something in Designer so that correct display name shows up?

or 

Any other suggestion.

Thanks in Advance