I am not sure about Chrome, but I have a feeling it was able to remember my username for most sites.
As for anonymity, it really depends on what you mean. Anonymity in the strictest meaning is actually a misnomer. To achieve anonymity, you could not select any username at all. Anonymity means not even two of your posts on the same site can be linked together. So you would not register at all.
Pseudonymity is when you have an identity for certain purpose, that can't be linked to your real identity. There are many "levels" of pseudonymity, you can have one pseudonym for everything on the internet, just not under your real name. You can have different pseudonym for each site or even each user you communicate with. The last one meaning if you send me two messages, I can tell both are from the same person, but if you send a message to my friend, we can't know, whether both were from the same person or not.
Whether you choose to be anonymous or pseoudonymous and at what "level" or type of pseudonymity depends entirely on what you are trying to achieve. Do you care that people can link the identities together? Are you worried you may leak your real identity or clues and you don't want that to "spread"? Do you want people to be able to recognize your username? It is up to you and your preference.