Deputy First Minister John Swinney held talks with public sector bodies and charities to begin changing the draft law.
The Named Person scheme was found to be against human rights legislation which guarantees the right to a family and private life.
The judgement said: "The first thing that a totalitarian regime tries to do is to get at the children, to distance them from the subversive, varied influences of their families, and indoctrinate them in their rulers' view of the world."
The flagship SNP policy set out to appoint a single point of contact, such as a teacher or health visitor, to look out for the welfare of children under 18.
Supporters say the scheme would protect vulnerable children, but others say it undermines the role of parents and is a creeping attempt by the state to replace the family.
After the defeat in the Supreme Court the SNP vowed to press ahead with the legislation, saying it would amend it to be compatible with human rights law.
John Swinney MSP said: "Our aim has always been for the named person to provide timely support for children and families. We have always said that as part of that role, we expect that any sharing of personal information should be proportionate and relevant.
"The Supreme Court's ruling makes clear that while the principle of providing a named person for each child does not breach human rights, we need to do further work to ensure those performing the role have greater clarity about sharing information, as required by the Court.
"I have already spoken directly with senior figures from the public and third sectors including NHS, local authorities and Police Scotland to discuss our next steps.
"We will continue these discussions, including with professional bodies, to use the expertise of those working directly with children and families as we move forward with our plans."
After the ruling on Thursday Simon Calvert from the Christian Institute told Premier: "It's a pretty serious business when a government is told by the Supreme Court of the UK that they've passed legislation that breaches the privacy rights and human rights of families and children. It's a big ruling and we're delighted.
"The Scottish Government is in denial. Anyone who's read the judgment knows that we won and they lost - the appeal was allowed.
"The Scottish Government ought to have a period of reflection and a bit of humility, really."
