I'm not sure what you're trying to achieve with this query (ParallelPeriod is usually used in conjunction with an aggregation to give a value) but if you just need the measures to display what they are then you can append them with .Name, like so:

WITH MEMBER [Measures].[Previous Period] as

( ParallelPeriod(

[Date].[Fiscal].[Fiscal Month] -- Level to traverse

, 1 -- How many members to go back on the Level

,[Date].[Fiscal].CurrentMember )).Name

MEMBER [Measures].[X] as [Date].[Fiscal].CurrentMember.Name