Tradeoff between Consistency and Uniqueness in choosing publication Last Name
If your full name, or initials with last name is common in your field, there might be some inconvenience. But otherwise I doubt that uniqueness has much value. I share a full name with another prominent researcher but in an entirely different field. It is sort of funny when the search turns up both of us, but it is obvious that we are different people.
Consistency, on the other hand is very important, though at the very beginning, the earliest papers may not be so important to the overall career trajectory. But, by the time you finish a doctorate you should establish a name that you can live with throughout your career. Hopefully your earliest work won't be your best work over a long career and a few exceptions won't be an issue.
A personal web site (or one hosted by a university) can be useful in pointing to your work, even if done under different names initially.

For the record, it should be noted that some people publish under a pseudonym to maintain both uniqueness and consistency.