Order database view in new columns
This code should get your sorted.  Note: the top portion is just to set up sample data.

This will include a row if there is a vendor, but no vendee (VE will be null).  It will not include a record if there is a vendee, but no vendor.  

-- You Sample Data
WITH YourTableName AS ( 
    SELECT * FROM (
        VALUES ('JAKE' , 'VO'  , 1234)
                ,('JOSH' , 'VE'  , 1234)
                ,('ANNA' , 'VE'  , 1212)
                ,('FAYE' , 'VE'  , 1212)
                ,('MATT' , 'VO'  , 1212)
    ) AS V(NAME, REL, ID)
)
-- Your View Text, replace 'YourTableName' with... wait for it... your table name:
SELECT VO, VE, Vendor.ID, COUNT(*) OVER(PARTITION BY Vendor.ID) AS CNT 
FROM 
    (SELECT Name AS VO, ID FROM YourTableName WHERE Rel = 'VO') Vendor
        LEFT JOIN (SELECT Name AS VE, ID FROM YourTableName WHERE Rel = 'VE') Vendee
        ON Vendor.ID = Vendee.ID
ORDER BY Vendor.ID DESC, VE  -- Can be included, really need to be specified when querying the view