What you are looking for is commonly referred to as a junction object representing the many-to-many relationship here.
Here is an example from trailhead about a junction object being used in a job posting scenario for a recruiting application: https://trailhead.salesforce.com/en/content/learn/projects/build-a-data-model-for-a-recruiting-app/junction-object-job-postings
Your object would have two lookup fields on it. One to Goal and one to User. These junction records allow you to link one goal to multiple users and similarly one user could be associated to one or more goals. If you need to represent a user's role related to the goal, a third field on this junction record could be added to capture Role.
You might name this object Goal Assignments.
Contrary to what you may have seen in a forum, you do not need a lightning component to implement this pattern.