There are several search terms that can be used. I don't know all of them, but here are some from the top of my head.
- Abbreviations. (There's not an abbreviation for every item)
- RoA (Rod of Ages)
- IE (Infinity Edge)
- DFG (Deathfire Grasp)
- LT (Liandry's Torment)
- Other search terms
- Spooky Ghosts (Twin Shadows)
- Tons of Damage (Trinity Force)
- Pink Ward (Vision Ward)
- Green ward (Sight Ward)
- Stark's Fervor (Zeke's Herald)
You can also search for stats, such as Attack Damage or Health Points. For example, searching for "AD HP Armor" would bring up any items that provide Attack Damage, Health, and armor.
Certain items have descriptions. Searching for their description may also bring up the item.
There are probably more search terms and I'll try to add them if I remember any more.