Huh, that's a good point. A better universal naming system would be something like "Base x+1", with x being one integer lower than 10. So humans would use Base 9+1, and the alien would use Base 3+1.
*This has been on my mind all day and the more I think about it, the more obvious it becomes how fundamentally terrible the name "Base-10" is. How did this never occur to the people who coined the term? Even the system I suggested is flawed as it's still trying to incorporate the same bad logic.
A better system would be something like Base 9, stopping shy of the respective 10 in each system, or if it needs to be clarified, Base 9+0, as 0 is the extra digit in the first place, not 10.
let there be any base "b"
That can represent a number by the sum of their positional digits:
number = sum(d_i * b ^ i)
where i is the position index and d_i is the digit at this position. (note: index starts with 0, from the least digit farthest to the right)
The most reliable way to communicate bases would probably be using unary.
Now if your alien is using unary, that might not work, but it should for all higher bases.