What is the name of the detective inspector who often investigates cases with Sherlock Holmes?

The detective inspector who often works with Sherlock Holmes is Inspector Lestrade.

Lestrade is a Scotland Yard officer who appears repeatedly in Arthur Conan Doyle’s stories. He is capable and experienced, but Holmes’s unusual methods and superior powers of deduction often leave him unable to solve cases independently. Even so, Lestrade is usually willing to recognise Holmes’s expertise.

The inspector first appears in A Study in Scarlet, alongside another Scotland Yard detective, Gregson. Their rivalry is part of the early novel’s depiction of conventional police investigation. Lestrade later becomes one of the most familiar recurring police characters in the canon.

His first name is generally given only as an initial, “G.” Doyle’s stories do not establish a universally accepted full name, which is why “Inspector Lestrade” is the safest canonical identification. Adaptations have supplied different personal details.