stored procedure update retain values In SQL Server, when using optional parameters, the only way to have default values is using @param = NULL upon creating.

Is there a way for the stored procedure to know that the application will only update specific columns and the remaining columns will retain the original values?

Here is my example:

Data: col1 = "AA" col2 = "BB" col3 = "CC"

Application update inside stored procedure: UPDATE table SET col3 = "C", col ="B" WHERE id = 1

After update, value of col1 will remain.

I hope my explanation is clear enough :)
If I understood correctly, if stored procedure is called with @vCol1 = 'AA', @vCol2 = 'BB' and @vCol3 = NULL then you want to update only Col1 and Col2 keeping the Col3 value intact.
Then you can go with the following solution. I agree its not the best one but it will get work done in simple manner.

UPDATE table
SET col1 = ISNULL(@vCol1, col1)
  , col2 = ISNULL(@vCol2, col2)
  , col3 = ISNULL(@vCol3, col3)
WHERE id = 1