Is there a formal term for the placement of two symbols next to each other to imply an operation?

In abstract algebra, when words are formed using letters from an alphabet, the operation of joining two words together with no symbol in-between is called concatenation.

Now I wouldn't recommend that in a case where the left and right sides are mathematical objects of a different nature. In that case, it seems that juxtaposition is fine - I have seen it used at least a couple of times, and I don't feel that it carries a connotation in a mathematical context. And if you want to be extra clear, you can add some words the first time you use it, in a footnote for instance.

You are correct about juxtaposition. The Wikipedia article Order of operations has this sentence:

However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division

which indicates that this juxtaposition is used in the context of precedence of operators in mathematical expressions. It is all in the associated context and defined by conventions. You can use, modify, or create your own conventions as long as you explain what you are doing.

The third term I have heard for this is apposition, as in "two symbols written in apposition".

(However, I concur with the other answers that juxtaposition is perfectly understandable.)