For males, I would put the original surname in "Last Name at Birth" , and the adoptive surname under "Current Last Name." For Females, I would put the surname at death in "Current Last Name," and the adoptive surname in "Other Last Names". However, this is a matter of personal choice. You may choose to put the adoptive surname in "Last Name at Birth" if you prefer.
In either case, you will want to document and explain everything in the Biography, and provide links there to whichever set of parents you did not link to using the Fields.
To quote the section on Multiple Parents in the Help files :
WikiTree only allows a person to have one mother and one father. This provides the basic structure for family trees.
What about adoptions and step-parents?
Here's what we recommend:
Put whichever parents you want in the family tree. It doesn't need to be the biological parents. It's your choice.
Link to the other parents in the Text/Biography section. For example, on Rex Sample the text includes:
Rex was adopted by his grandmother [[McTester-95|Maddie McTester]] at a very young age.
On the grandmother's page we also added:
Maddie adopted her grandson [[Sample-4|Rex]] and raised him as her own.
This way everyone is connected and the relationships can be clearly explained.