Opening a credit card for someone else to use…is it a bad idea?

I live in the US and my parents do not, they visit often and shop online frequently and currently use my CC when they do (to avoid fees and exchange rates associated with using their own cards).

It’s become a little difficult to separate their transactions from mine so we can settle up each month, and for simplicity’s sake I was thinking about opening up a new CC in my name that is just for them to use.

Any obvious issues with this plan?