The system is set up to default on your name. If you select recents, the first name that appears after your name is the last name you were working on. Hope this answers your question.
I use the RECENTS list that Brett discusses all the time - thats how I get back to the last person I was working on.
When I sign in, I am brought to a home page. In the right hand column there is a box labeled Recent People. You should see the last people you viewed in that box.
So it does!
Thank you Carol Ann.
Short Answer: "Technically" you CANNOT ...
'Family Tree" of 'FamilySearch' is NOT set-up to work that way.
That said ...
There are a couple of possible 'Work Arounds' ...
Your "Recents" LIST records a number of the last individuals/persons that you worked on ...
The TOP of that LIST is YOU ...
The NEXT individual/person DOWN is the LAST individual/person you accessed.
This is the best and most simple option.
Here is a "Knowledge Article" in 'FamilySearch':
How do I find the records I last viewed in Family Tree?
(2) "Family Tree Starting Person"
You can "Change" the "Family Tree Starting Person" in the "Setting" of your 'Account'.
This would be vey tedious; as, you would have to "Change" the "Family Tree Starting Person", in the "Setting" of your 'Account', EACH and EVEY time.
How do I change the starting person in Family Tree?
(3) Of course ... you could always "Bookmark" the "Person/Details" page/screen of particular individual/person each time.
You would have to constantly "Clear" the OLD and unnecessary "Bookmarks" frequently.
I hope this helps.
If you want to always start with the same person for an extended length of time, you can change the default person that appears at the root of your family tree in the family search.org Settings area: