1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be $n$.
Therefore, using $n$ alphabets we can form $n × n × n = n^3$ distinct 3 digit initials.
Note: Distinct initials are different from initials where the digits are different.
For instance, $AAA$ and $BBB$ are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This $n^3$ different initials $= 1$ million
i.e. $n^3 = 10^6$ (1 million $= 10^6$)
⇒ $n^3 = (10^2)^3$
⇒ $n = 10^2 = 100$
Hence, the language needs to have a minimum of $100$ alphabets to achieve the objective.