This question is very nearly a duplicate to "Taking an academic pseudonym?", however, my name is already sufficiently unique, and I am wondering if it makes sense to use a pseudonym even if I don't need to? (Perhaps this is too subjective for stackexchange...)
I have a (potentially unfounded and/or irrational) fear of publishing on my official name, which is also the name I use in social situations. This is partly since I am at-present "un-Google-able" and I'd very much like to stay that way. I'm thinking about this a lot now since I am soon going to publish my first paper, and I know that it's important to have a consistent academic identity.
Suppose my full name is "Sheldon Lee Cooper", and I normally go by "Sheldon Cooper". I've been thinking I could publish under "Lee Cooper", and then Googling "Sheldon Cooper" would still return no results. I'd use "Lee Cooper" on my academic webpage too, and I would ask to submit my PhD under this name also.
Alternatively I could publish under "Sheldon Lee". (As in this answer.)
My academic research is focused on a niche area of (pure) mathematics, so am I being irrational in wanting to remain somewhat anonymous on the internet? Should I acknowledge that publishing niche mathematics is unlikely to harm my reputation and just publish under my legal name as-is? Or does it makes sense to publish under my middle and last name, or even an entirely unique pseudonym? What are the advantages and disadvantages either way?
Some related questions I've seen on academia.stackexchange include:
Pen name similar with real name: Zu Yangzu instead of Zu Yang for papers
This is about having a unique name. My name is sufficiently unique in either variation.
Is it possible to be known in academia by a different name?
Short answer: Yes.
If I publish under a pseudonym, can I still take credit for my work?
Short answer: Probably yes, though not fully anonymous in that case. This will become your academic identity.
Separating academic identity from social identity
My scenario differers in that I currently have no Google results, and if I publish under my own name then that will become my Google results. If I take up publishing erotic novels then I am in a position to do that under a pen name that doesn't conflict. So I don't already have a different identity conflicting, as the author of this question does.
Taking an academic pseudonym?
This is very similar to my question, the key difference being that the author has the motivation of avoiding confusion with other people who have a similar name. My only motivation is fear of being Googled easily (in a non-academic context). Is that fear irrational?