Last time I checked, accidental meant "happening by chance, unintentionally, or unexpectedly."
The way I see it, looking for a name that was "suspicious" means that making it sound suspicious was the goal from the start, naturally leading to the anagram. That doesn't sound accidental to me, which is what I think of when someone randomly stumbles into something.
Well apparently the anagram is just an accident.
Based on the scans:
「怪しくてかっこいい名前になるように考えたら、
偶然にも例の彼とのアナグラムに」
Basically loosely translated as 'while thinking of a mysterious and cool name for this character, it accidentally happens to be anagram of the main character'
Edit: More akin to 'we are looking for cool name, found one, then found out that it's an anagram'