Chainalysis' main client are government departments as they offer tracking services that can potentially rule out the crime happening with the use of cryptocurrencies, I don't see any private companies availing their services as there is no need for them to do so. Regarding if Chainalysis have any close competitors with what they are doing I don't recall any name competing against them so they are literally the only ones who stand out in this Blockchain tracking industry, however I think for a main competitor to rival Chainalysis in this industry I see the biggest opportunity for them is to discover a way on how to track Monero related transactions which I think the US government particularly the IRS have provided a reward for people on cracking Monero's system. If they simply did this first then I think it will pave them the way to overtake Chainalysis.
I reckon there were
claims that Monero’s anonymity and privacy were cracked, however, none has shown proof of this. I reckon the American government would be more effective to use the reward money to pay internet trolls to spread fear, uncertainty, doubt to discourage the people from using Monero hehehehe.