Using different username and different email for every gambling account is good but I dont get the idea how it can be related to revealing our identity in the internet.
For me it is more for security purpose, I used to use the same username (the one I use as my bitcointalk username) but with different emails, and its been more than 10 years I use this username for almost my online account.
Well, you can use the same email and username at different gambling sites but it is not recommended to use the same password across all sites. 99% chances there won't be issues in using the same passwords, but consider you are also playing at any untrusted new casino or there are any bad characters in some casino. They may somehow get your password and try to login on other gambling sites and may succeed if you have the same passwords on every site. Although this may not happen often, but why take risk for even 1% chance of this being tried by any scammer.
Each gambling site has additional security features. So, there is a small chance they can access our account only with the email or password that we create on an untrusted gambling site, which has the possibility of hacking or misusing customer data.
I habitually use a different username for each gambling platform I create, but I still use the same email with a different password.