Are these sentences correct:
1 The dog has a chip in his neck to show who his owner is.
Meaning: The dog has a chip in his neck which shows who his owner is.
2 The computer has a tag on it to indicate when it was fabricated.
Meaning: The computer has a tag on it which indicates when it was fabricated.
The meaning is right but your use of "fabricated" is not natural. We would just use "made" or "built".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.