From what I understand, these watermarks generally show up in Alpha/Beta/Early Access games.
Generally, they all have a similar format, consisting of some sort of unique identifying number; often along with the game name, the beta version, and your username.
There can be multiple uses for this.
Bugs/Information - The watermark can provide build information, and perhaps other information about what program version is running. This can make troubleshooting a lot easier when provided with a screenshot of an issue.
NDA/Privacy - Some games initially release under non-disclosure agreements and have very strict rules about sharing game information outside of approved channels. By including watermarks; you can mitigate the ability for people to leak content that you don't want released. It becomes easier to track down who released it (they might have more subtle ways too, but this lets the user know they can find you).
Based on the fact that most full-release games I've seen opt to not include this, I would think these are the two primary reasons.
I considered it as advertising the game and watermarking screenshots to be a third reason; but anyone who wants to steal your content could easily cut that part of the image out. I think that's a fairly unlikely motivation.
Best Answer
I don't believe there is a specific spawn rate, however from experience I'm pretty sure there is a 60% spawn rate.