Many of the figures in Norse mythology are known by several different names, as well as different phrases that describe them (called kennings). The following is a list of some that refer to Loki, and I will update the post accordingly as I find or am informed of others. A lot of the kennings provided by Snorri are found nowhere else, and are somewhat inconsistent, so I only included a few.
Loki’s Names: Gammleid (leader of amusement), Haloge, Hvedrung (roarer), Lodur, Logaþore, Loge, Lôgna, Logi, Lokkji, Lopt (lofty)
Loki’s Kennings: brother of Byleistr, brother of Helblindi, blood brother of Odin, confidant of Thor, friend of Odin, friend of Thor, fromkveda flaerdanna (seductive speaking), gift bearer, harmer of Sif’s hair, laugaz (blazing god), laugatjanaz (blazing one), prisoner of Geirrodr, rogur (slanderer), scar lip, sea thread’s father (the sea thread is a kenning for the Midgard serpent), sky walker, slaegi (sly), slaegurtyr (sly god), staunch friend of Hoenir, thief of brisingamen, thief of giants, thief of Idunn’s apples, vaelandi (debasing), wolf’s father
Bonus: One kenning used to identify Thor is bragdmilldr Loka (compassionate to Loki)