Answer:
A carved file, by definition, is a file that is not recorded in the file system records but can found within another data stream.  Carved files do not have names or metadata, so FTK assigns its own names.

FTK 2 and later:

FTK 2 and later assign names like "Carved[xxxxx].jpg".
The number within the brackets is the byte decimal offset count from the first byte of the parent file from which the file was carved.

Examples:
File name: Carved[12345].jpg
Path: Mantooth2.E01/Partition 1/MANTOOTH [NTFS]/[unallocated space]/006350>>Carved[12345].jpg
Interpretation: The carved file was found beginning at decimal byte offset 12345 within the unallocated chunk "006350".

File name: Carved[789].bmp
Path: Mantooth2.E01/Partition 1/MANTOOTH [NTFS]/[root]/Documents/MyFile.doc>>Carved[789].bmp
Interpretation: The carved file was found beginning at decimal byte offset 789 within "MyFile.doc".
 
https://s3.amazonaws.com/cdn.freshdesk.com/data/helpdesk/attachments/production/69009877462/original/inline1078951359.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAS6FNSMY2XLZULJPI%2F20210926%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20210926T171548Z&X-Amz-Expires=300&X-Amz-SignedHeaders=host&X-Amz-Signature=55becdab7466afdacc2f647a6df9874c090eb75048529885332b2295e95eb183

FTK 1:

FTK 1 assigns names like "AAA_xxxxx[yyyyy].bmp".
AAA is the file type/extension.  xxxxx is the byte decimal offset count from the first byte of the parent file from which the file was carved. yyyyy is the parent file's item number.

Example:
File name: JPEG_12345[543].jpg
Path: Mantooth2\Part_1\MANTOOTH-NTFS\pagefile.sys>>JPEG_12345[543].jpg
Interpretation: The carved JPEG was found beginning at decimal byte offset 12345 within pagefile.sys (which is item #543).