Yes, Answer is yes to both questions. Move an index is similar to the process of backup and restoring indexes. Regarding renaming an index I have never don't it but hopefully the links will help you. Dont forget to make sure file system permission are set correctly when migrating.
Here are some docs that will help:
Hope this helps or gets you started. Dont forget to accept answers and vote on answers that help.
I would gzip and rsyn the directors over to the linux server in the appropriate directory. Make sure ur migrated index is set in the indexes.conf.. Set your permissions use cown and chmod. Both servers must gave splunkd stop while doing this. Permissions need to be correct as ntfs perms will not match or carry over.