C# SqlCommand - cannot use parameters for column names, how to resolve?

As has been mentioned, you cannot parameterise the fundamental query, so you will have to build the query itself at runtime. You should white-list the input of this, to prevent injection attacks, but fundamentally:

// TODO: verify that "slot" is an approved/expected value
SqlCommand command = new SqlCommand("SELECT [" + slot +
           "] FROM Users WHERE name=@name; ")
prikaz.Parameters.AddWithValue("name", name);

This way @name is still parameterised etc.

You cannot do this in regular SQL - if you must have configurable column names (or table name, for that matter), you must use dynamic SQL - there is no other way to achieve this.

string sqlCommandStatement =  
   string.Format("SELECT {0} FROM dbo.Users WHERE name=@name", "slot");

and then use the sp_executesql stored proc in SQL Server to execute that SQL command (and specify the other parameters as needed).

Dynamic SQL has its pros and cons - read the ultimate article on The Curse and Blessings of Dynamic SQL expertly written by SQL Server MVP Erland Sommarskog.