Definitely bad timing. My experience with names: they are never good enough.

What I look for in a name:

1. If I say it out loud, you know how to write it.

2. If I say it out loud today, you remember it tomorrow.

On that 2 criteria, Riot works quite well I think.

It's bad in that there's already a very popular game company named Riot (Games) which everyone refers to as 'Riot'.

Disagree, I have serious doubts you could confuse the two. I can see almost no context where 'Riot (Games)' and 'Riot (Anti-Phish Company)' could be meaningfully confused.

Some people know League of Legends, most don't know Riot Games. And I double checked: Riot Games don't own a trademark for anything related to cybersecurity.

Unfortunately that doesn't seem to stop them going after companies with Riot in their name (even though Riot is also a dictionary word) :(

Way more people already know riot games and league of legends than will ever know about your security startup, so I don't see what they're upset about for you. Hand-wringing, perhaps?