Different entry URL but same page objects - tests failing

Good day,

Kindly help me understand what's going on and how to resolve this.  So far, I have created and successfully run my tests using this 1st url: https://ismads-qa-test.vestcom.com/

Due to environment update from Dev, we now need to run the same tests but using this url: https://vestcomportal-test.vestcom.com/

After reviewing the Mapped Objects and Aliases, I suspect that we need to re-create (record new & separate keyword tests) using the newer url in order for TestComplete to work its magic???  I was hoping to implement a simple "test parameter" to change the url at run-time.

See attached for details.  In the first image, the hint says to: Consider updating the identification properties to use the similar object. Let's say I do update it - will the same test work when we need it to use the 1st url?  How would you set your tests up so that we can reuse the same test steps for each of these 2 urls?

Thanks very much,

Arlene