Edit the Survey Termination in the Survey Options section to create a custom end of survey message. In this message you can create the link to the new non- anonymous survey to collect contact info.
If you are concerned about users finding this contact info survey without completing the original survey you could put a HTTP Referrer restriction on the contact info survey, https://www.qualtrics.com/support/survey-platform/survey-module/survey-options/survey-protection/#RestrictingWhatWebsiteARespondentComesFrom

Thank you so much I will do so.

Further to my question about linking 2 surveys. It seems that participants who declined participation and who are not employed are also directed to the lucky draw link at the end of the survey. How do I prevent that. Can I have two options for end of survey and use skip logic?

My survey is on employees who study. However employees who study can take the survey and those who are not studying can also take the survey as I am interested in the difference of experience.
If a participant says that they not studying, there are many questions that then dont relate to them, is the best option to use display logic - and can I use that for a block of questions?

You can use Branch Logic, https://www.qualtrics.com/support/survey-platform/survey-module/survey-flow/standard-elements/branch-logic/, to direct the users to different End of Survey elements with different custom end of survey messages.