SSIS Expressions have a very limited set of functions. If I remember correctly, it offers the functions that were available with VBScript way back when. There are no string formatting functions even in 2016 according to the documentation and people end up concatenating the various parts of a string.
You can use a Script step though to format a date using String.Format and store the result in a variable, as shown in [Using Variables in a Script Task] (https://msdn.microsoft.com/en-us/library/ms135941.aspx) and this SO question, eg:
var targetFolder=Dts.Variables["User::targetFolder"].Value;
var filePrefix=Dts.Variables["User::filePrefix"].Value;
var someDate=Dts.Variables["User::myDate"].Value;
var filePath= = String.Format(CultureInfo.InvariantCulture,"{0}_{1:MMMM}.txt",filePrefix,someDate);
var fullPath=Path.Combine(targetFolder,filePath);
Dts.Variables["User::filePath"].Value=fullPath;
The advantage of a script task is that you can use all of .NET's functions to format values (eg String.Format) and manipulate paths (eg Path.Combine, Path.GetFileNameWithoutExtension etc)