It is named for its purpose.
Most instructions include the same addressing modes. The CPU architects call the work of determining the memory address selected by the addressing modes as "computing the effective address".
The instruction purpose is to put the effective address into a register. Hence, "load effective address".
Yes, it is true "it just performs arithmetic". If you think about it, that's pretty much all a CPU does, so that phrase isn't very descriptive of any particular instruction or CPU activity.
If you want to understand how many instructions get their names (let alone what the purpose of an instruction is), it is a good idea to take a computer architecture class.
[Edit after long comment interaction, below]:
Most of the answers here (including mine) were hung up on "computing effective addresses", in which the instruction is used to form a memory address, where the instruction has a well-deserved name.
However, since the instruction doesn't actually use the computed "address", another
extremely common use of the LEA instruction is simply do the arithmetic that it does. In effect, LEA viewed from this perspective is a combination of compute sums or products with some special small constants, and store the result to another register without affecting the condition bits. It also happens to do this very quickly compared to doing a real multiply. The utility of this in real programs is surprisingly high; get some experience writing assembly code on x86 and you will believe this.
So LEA can be used, for example, to multiply a register by 5 and add a big constant. Here the instruction name only confuses; unfortunately, it still has to have a name.
Welcome to assembly-code land, where designers invent instructions to achieve one purpose, and coders discover that they can use the instruction to compute things the designers didn't obviously consider. [The AND-immediate instruction is pretty handy for computing modulo some-power-of-two, as another example]. So every instruction in a rational instruction set was placed there by the instruction architect becuase it serves some useful purpose. And it gets use for that, and other things, as coders discover clever applications.