It all depends on the office culture.
My old job (private church) school had 30-40 employees, and we had secret pals or prayer pals for the semester. You could choose one or neither.
At orientation, the tech/admin person passed out a form where you could fill in your favorite snacks and drinks, what you wanted or did not want, fave colors, etc...
For prayer pals, it was more personal, with family details and specific prayer needs that could be shared if you wished on the form.
These forms were tweaked every couple of years until they were fine tuned and almost error-proof if you followed what was written by the pal you drew.
(I worked here over a decade. It was not intrusive and I am still friends with many people there. SP gifts were fun and it added to work enjoyment. That, and the fact that the director often came around door to door during naptime/quiet time with bite-sized chocolate and/or candies for the teachers!)
The it/tech made copies of the forms and then kept track of who drew who, by having the recipient write their name on the outside of the folded up paper. When a teacher moved away, she re-assigned with permission and all was well.
When I subbed in a jr high last December when a teacher quit abruptly, I knew the girls' homeroom I was suddenly in charge of needed extra love and attention. I assigned secret santas and made sure each girl knew to gift each other. I also came in each morning and added a small treat to their in my room locker stockings, whether a mint, a hershey's kiss, a Christmas pun, a small candy cane, a pencil grip eraser, etc...
When one girl reported that after a few days she had not received anything from her pal, I discreetly asked the giver if she had forgotten, to learn that she was planning a bigger gift at the end instead of little gifts leading up to the last day breakfast party/reveal. No feelings hurt, and all was well.
Both times it took time and organization and care and reminders.
I would not expect a business full of adults that may not interact with each other even at lunch to suddenly feel led to give awesome gifts, especially if the one in charge of the pal'ing does not lay out careful expectations.
gift range (say $5-$8, or $20-$25)
Be aware that value and cost are not the same
some standard line about non-discrimination/harassment, be professional, etc...
you WILL be revealed