What should I use instead of "prefixed with"?
Solution 1:
You are talking specifically about a prefix. You need to use the word prefix, because precede and preface do not have to mean that something is actually attached. Prefix is the only thing that means this. There is nothing wrong with prefixed with in this context. As a linguist who deals with prefixes and suffixes as a central part of my work, this phrase is something I use regularly. However, if you want an alternative, you could say something like:
The function name must have ### as a prefix.
Solution 2:
I hope this will be explanatory:
- The string “__” must be prefixed to function names.
- Function names must be prefixed by (or with) the string “__”.
Solution 3:
First of all, I believe the original usage "must be prefixed with" is the best available construction here, and you should ignore the software's recommendation.
That said, I would guess that your grammar checker is flagging that phrase for passive voice, even though its suggestions don't address that issue. To recast in active voice, you could either use something like what you have in your question -- "the function name must start with a prefix" -- or "you must prefix the function name with..."