You have a Name field that is the person name and also you have each records cretion timestamp.
So Add a script
sort by Meetingpeople::Name[Asending/Descending]
For ist time if you want to sort by Name and for 2nd it will be by creation time then make a if....else script and in else part just add this
sort by Meetingpeople::CreatinTimestamp[Asending/Descending]
Thanks Atauf. That's what I had tried.
Here's the script I have.
Go to Portal Row [Select; First]
Sort Records [Restore; No dialog] (The sort was - MeetingPeople::Person_FullName)
Refresh Window 
But that didn't make any difference
There are two way to do it
Make two tab(Hidden) named as Port1 and Port2
In port1 portal setup sort record by its cretaion Timestamp field
In Port2 portal setup sort record by its MeetingPeople::Person_FullName
Then create a script such a way that when user click on that SORT button then it will navigate to the Port2 tab.The default tab must be port1.
The portal showing in that layout is coming form the realtionship.So make a duplicate relationship with the same fields.
1>Sort 1st realtionship by its name
2>Sort others to its creation Timestamp
Make two hidden tab and in each tab put the related portal from the relationship and Default tab must be the portal sorted by the Creation Timestamp field.
Run the script having only one step e.g go to object port2 like FIRST way.
NB:As the tabs are hidden,the user will not get any info regarding this.
Hope you will get your solution.