Long story short: Varig Log was the Cargo/Logistics branch from the former Varig Group controlled by parent company "Fundação Ruben Berta" - short FRB-Par (which also owned the Varig passenger service brand as well as other companies such as SATA Ground Handling Service, VEM Varig Engineering and Maintenance, etc.). Due to Varig's financial problems, the parent company sold the Cargo/Logistics branch to Matlin Patterson. As that still didn't solve any problems, a part of Varig passenger services (called "Unidade Varig Produtiva" - UVP", which was nothing else than the operational side only) was sold to Matlin Patterson back in June/July 2006 which also held the right for the brand name Varig (among other things). As Matlin Patterson now controlled the 'almost original' Varig (which has become a completely new airline by now - she's known as the "New Varig" nowadays) there was no need to change Varig Log's name.
Three days ago the "New Varig" was sold to Grupo Áurea (who also owns the LCC Gol in Brazil)... So, it's not unlikely that Varig Log will be rebranded soon (unless she's sold too). Quite possibly to "VELOG", which is how Varig Log is commonly know back here in Brazil.
Ok, hope this helped
Hya! Yep, this livery is really something! Can't wait to see the next one in this livery - if they keep the livery
"When it's dark enough, you can see the stars" - Charles A. Beard