Usually that kind of metadata is created by the camera (e.g., some cinema cameras, such as most of the ones by Blackmagic Design, can automatically create incrementing take numbers in the clip metadata as you’re shooting; they also give clips incrementing file names that include the date and time shot, which can be used to organize clips by shot order). I don’t see anything in the Resolve manual to indicate that it’s possible to set take numbers in the metadata of a group of clips to increment automatically.
If your clips’ filenames are date-stamped or include some other kind of incrementing information, you can filter by filename to organize your clips by shot order, but it looks like you’d have to enter metadata like take name by hand.
I bet it’s possible to write a script for this, and you’re not the first person who has asked for this feature. It might be worth adding it to the “suggested features” section of the DaVinci Resolve section of the Blackmagic Design users’ forum.