Additional credit cards

Many (if not all) card issuers offer additional cards for family members - ie two cards for two people but on the same credit card account.

Is it possible to get an additional card in the same name as the main one? The reason I ask is that I have two wallets (a work and home one) that contain different sets of 'stuff' but I could do with having my credit card in both.

Is this an unusual request!? :o