You want the OUTPUT clause

UPDATE Items SET Clicks = Clicks + 1
OUTPUT INSERTED.Name
WHERE Id = @Id

Accesses table only once :

DECLARE @Name varchar(MAX);

UPDATE Items SET Clicks = Clicks + 1 , @Name = Name WHERE Id = @Id;
SELECT @Name;

If you're using SQL Server 2005 onwards, the OUTPUT clause is ideal for this

Use a Stored procedure for this.

Create a stored procedure that takes the @id as a parameter and does both of those things. You then use a DbDataAdapter to call the stored procedure.

I could not manage to update and return one row inside a select statement. I.e you can not use the selected value from the other answers.

In my case, I wanted to use the selected value in a query. The solution I came up with was:

declare @NextId int
set @NextId = (select Setting from Settings where key = 'NextId')

select @NextId + ROW_NUMBER() over (order by SomeColumnOfYourTable) from YourTable

update Settings set Setting = Setting + @@ROWCOUNT 
where key = 'NextId'

I needed this in sqlite.

In sqlite you can do this by using the Returning clause.

UPDATE Items SET Clicks = Clicks + 1
WHERE Id = @Id
Returning Name

For more info see: https://www.sqlite.org/lang_returning.html

You can also return all fields like this:

UPDATE Items SET Clicks = Clicks + 1
WHERE Id = @Id
Returning *