The bank may run a credit check on you trixie, but this is unlikely - as your company is the ultimate payer. I have company credit cards in my group, and we are careful who we allow to access them - but it I had a trusted employee who had historic financial difficulties, there is no way I would have a problem in allowing them use of the cards if there was a business case.
If you are at all worried, you could explain to your boss that you don't want your name to be on the card, but you are happy to be named user. This would then not involve any form of credit check, unless the bank had a specific policy on this.
Regards, Melanie Giles, Insolvency Practitioner