Why does the Cream song "Badge" have that title?

Because of George Harrison's poor handwriting.

https://en.wikipedia.org/wiki/Badge_%28song%29

"Badge" was originally an untitled track. During the production transfer for the album Goodbye, the original music sheet was used to produce the liner notes and track listing. The only discernible word on the page was "bridge" (indicating the song's bridge section). Due to Harrison's handwriting, however, Clapton misread it as "badge" — and the song was titled soon thereafter. Harrison remembered the story differently: "I helped Eric write "Badge" you know. Each of them had to come up with a song for that Goodbye Cream album and Eric didn't have his written. We were working across from each other and I was writing the lyrics down and we came to the middle part so I wrote 'Bridge.' Eric read it upside down and cracked up laughing-- 'What's BADGE?' he said.