SQL Server Full Text Search Engine is not returning consistent results
Took me a little while to see what now seems obvious. I can't seem to replicate your experience with John v. Smith on 2012, but if we check out the default system stopwords...

select * from sys.fulltext_system_stopwords
WHERE stopword = 'v.'


The result is

stopword    language_id
v.          1053


So it seems the stoplist is the problem. Let's try a blank one and see what happens:

CREATE TABLE [dbo].[fts_table](
    [name] [nvarchar](50) NULL,
    [id] [int] IDENTITY(1,1) NOT NULL,
  CONSTRAINT [PK_fts_table] PRIMARY KEY CLUSTERED 
  (
    [id] ASC
  )
GO

INSERT INTO [dbo].[fts_table]
           ([name])
     VALUES
           ('John v. Smith'), ('Bockelman v. MCI Worldcom, Inc.')
GO

--Pretend I scripted out the fulltext index creation here 

CREATE FULLTEXT STOPLIST [modified_stoplist]
AUTHORIZATION [dbo];
GO

ALTER FULLTEXT INDEX ON [fts_Table]
SET STOPLIST = modified_stoplist;
GO


Then the query now returns the results desired:

SELECT  *
 FROM CONTAINSTABLE(dbo.fts_Table, name, 
'FORMSOF(INFLECTIONAL, ''Bockelman'') 
AND FORMSOF(INFLECTIONAL,''v'') 
AND FORMSOF(INFLECTIONAL, ''MCI'') 
AND FORMSOF(INFLECTIONAL, ''Worldcom'') 
AND FORMSOF(INFLECTIONAL, ''Inc'')') 
   AS KEY_TBL


Returning...

KEY     RANK
1       32