K-fold Traveling salesman problem - A variant of TSP
There was a paper on the arxive last month, dealing with this generalization of the TSP:


  The multi-stripe travelling salesman problem
  Eranda Cela, Vladimir Deineko, Gerhard J. Woeginger
  (Submitted on 20 Sep 2016)
  https://arxiv.org/abs/1609.09796  


The problem does not seem to have a particular name in the literature.