I was bumbling about the Milwaukee Public Library World War I archives (which has tens of thousands of images, by the way—very cool) and I found this form (enlistment form? discharge form?) of one A. C. Niemann. There are thousands of ones like it, and a quick browse shows me that many mention a "name of pal" you can fill in. I know it's not the next of kin, as that has its own spot on the paperwork. Is this some sort of official pen pal?
Link to his particular form here: https://content.mpl.org/digital/collection/WWI/id/26432/rec/13
So this document doesn't look like a formal military or government one. It looks like it's some kind of index card from the Milwaukee Chapter of the War Mothers of America. The WMoA were a non-profit group started in 1917 to assist the war effort in any way they could. They did things like letter writing campaigns, fundraising, comforts funds and worked with the Red Cross. It was a way for women associated with soldiers, as it was made up of wives and daughters and sisters as well as mothers, to take part in the war effort. The form itself is presumably some kind that applicants would be able to fill out about their son, or husband/whatever, when they joined. Just an early form of database for people to use. It doesn't have his service number, which I find quite interesting, as that would have been an important piece of information to record.
"Name of Pal" I would assume is just that. The name of a friend to whom mail or inquiries could be sent or forwarded for information. If a soldier were illiterate something like that could be quite useful. I guess kind of like a military Next of Kin.
There's not a ton of information about the WMoA out there, but the Hathi Trust has digitised the book of the Proceedings of the First National Convention of the WMoA, 1918. It might have some further info if you can be bothered scouring it.