If you consider how credit cards are used there is no increased security risk associated with providing the bank employee with the card number and your name and address.
For example if you use the card for mail order purchases you will provide the same detail, but also the CVV code and expiry date a greater level of risk...but this is how they are intended to be used!
Similarly for any 'in-person' transactions, often the retailer will have full access to all the details from the card, albeit normally without address details.
Given that you are phoning the bank, by implication the person you are providing the details to is trusted by the bank...for the vast majority of subsequent card use scenarios there will not be as much trust in the person you provide the information to.
If the phone call requires you to 'authenticate' using a telephone banking password or phrase of some description, this can help to ensure that someone who has intercepted your post and stolen the newly issued card cannot activate it and use it.