A simple lookup of "concatenation" reveals 1,637 questions with that word in the post. Thus it is not uncommon on MSE with questions based around that topic.
Here are some suggestions. Below each question I have added some ideas as to the pros and cons of them.
Should the tag concatenation be added to the list of tags on MSE?
Based on the existing tags, I don't think there is one that covers concatenation. The closest one to concatenation that I can think of is decimal-expansion, but I think it is more common to mention the former than the latter (this opinion may be debatable). After all, the latter tag only has 820 questions.
Concatenation can also be with regards to strings and languages. The topics of abstract-algebraand automata come into mind here. Therefore in this aspect, there is not really a similar tag for it, at least from what I have searched.
The reason I suggest this follow-up question is that many of the questions that arise from the search query fall under the categories of either the concatenation of integers/primes/palindromes etc. or the concatenation of characters/languages etc.
However, there are some questions that are in neither category, so creating a different tag under the branch of concatenation each time would be excessive. I believe this would be the major drawback.
What does the community think?