To set up Governor Limit Email Warnings, check the below steps.
1. Log in to Salesforce as an administrator user.
2. From Setup, enter Users in the Quick Find box, then select Users.
3. Click Edit next to the name of the user to receive the email notifications.
4. Select the Send Apex Warning Emails option.
5. Click Save.
You can specify users in your organization to receive an email notification when they invoke Apex code that surpasses 50% of allocated governor limits.
how do store the limits in a custom object instead of sending it as email?
like when a user is exceeded the limit we will store those in a custom object and generate a report every week/month to see who is exceeding the limits and what limits are exceeded the most. so that we can know which limits to be increased in org or where do we have to do code rewamp.
Yes. You can create a error log object and store it. Sample Implementation: https://www.infallibletechie.com/2018/04/error-handling-in-lightning-component.html