That is not what the original post is about. @piccolini refers to apps that were transferred to the micro-SD card. In your case, this is the prompt you get when Android 6 first sees your card.
Selecting Portable storage will make it act as it was before, with Lollipop.
That means that the card can be read by other devices if you take it out of the phone.
Selecting that option will not format the card, the data will not be deleted.
The new mode Internal storage will format and encrypt the card so that nobody else can use it but the very phone that initialised it.
Only few people will want to do that as the micro-SD cards are usually way slower and less reliable than the 32GB embedded flash storage.
Android 6 properly displays the external card name, that is why you see some exotic name.
This name is originally given when the card is formatted. Because the card has to be formatted with a FAT file system, the name has a (very) limited length.
If you take out the card and put it in a computer/USB reader, you should be able to rename it.
Note that the card name should not impact the phone in any way. The proper way for apps to access data on an external card is not to rely on names. If an app cannot read what it could before, please double check that similar issues were not reported for this app (and whatever phone) before.
That is a very sound approach indeed.