Dan,we have a card each and then supplementary cards for each of us rather than what you are asking for.
All we do is code the charges to business and personal for accounting purposes.
Citi don't like business use phone calls at their call centre so just go with the flow. The less you tell them the better off you will be.
Citi has a very generous reward program so enjoy that part of using a Visa card on so many more things than an Amex card.
You can ask for a supplementary card without calling up.
Sign into your account, then go to "My offers" and then "Credit Card" where there will be an option to request a supplementary card.
You need to supply a name, DOB and address.
You can supply any name and I assume the DOB is only used to make sure the card holder is over 18.
As Cove said, business transactions are not allowed on the card so it would not be a good idea to have a second card in a business name however you could request the supplementary card with/without your middle initial so you can tell them apart.
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