Will my credit score be damaged by card issuers getting my name from a credit reporting agency and sending me an offer?
No. Your credit score is not affected by card issuers obtaining your name in this way.
If you apply for a credit card, the card issuer will generally obtain your credit report or your credit score and the credit reporting agency file will then reflect that you applied for a credit card. Your credit score can be affected by the number of cards or other loans for which you apply.