I keep both a written consultation card and a digital one on Phorest Salon Software. Will I be able to have just a client name and their colour on a card, no other details?

You will, but like any other personal data, this card will have to be stored securely in a GDPR compliant way. You’ll have to make sure that only staff who need to have access, actually do have access to it and that these cards are kept in a locked, GDPR-compliant filing cabinet. Using a digital consultation form or the treatment notes option on the client card might be safer.