OK, first, a query for a username should NEVER use LIKE. You want to return a single record, not a bunch of candidates, so LIKE has to be replaced with =.
Next, the parameter object will format the parameter for you so you don't need to add the single quote characters.
And why on earth are you listing usenames in a dropdown? That's giving away information to potential attackers. NEVER DO THAT! Use a textbox to get the user to enter their username, and even then NEVER directly pass the content of a textbox to a SQL query. It must be checked for having a valid value before being passed to the query.
string commandText = "SELECT Email FROM dbo.Users WHERE Name = @Name";
using (SqlConnection connection = new SqlConnection("nameOfConnectionString"))
SqlCommand command = new SqlCommand(commandText, connection);
command.Parameters.Add("@Name", SqlDbType.VarChar, 20).Value = UserNameTextBox.Text;