If you don’t have an LLC, you can use your personal credit cards, but the onus will be on you to separate the charges.
What we recommend is that if you are using personal cards, then designate one of your cards to be used solely for business expenses; it makes your expense tracking much easier.
Even if you don’t have an LLC, you can still open business credit cards with a DBA (Doing Business As) name so that the name appears on the bottom of the card, but that’s purely aesthetic since it’s still your social security number and your personal liability on the line.
If you have an LLC, then we highly recommend opening credit cards in the name of the LLC to keep your business and personal expenses separate and clean. There are other aspects to consider as part of the decision and we are happy to talk through them with you.