If you are a physical person shareholder having an Estonian limited company (OÜ) you would notice that your country of residence is reflected in the bottom of your annual report submitted to the Estonian Business Register along your size of shareholding.
Online annual report submission service automatically queries shareholder information from the Estonian Business Register. Currently Estonian Business Register service does not include a function to change shareholder's place of residence. This will be probably resolved in the new Business Register version that comes live later in 2021.
If you are worried about your place of residence being reflected in the company's annual report and you would like to change your country of residence you or your accountant can do it when submitting annual report.
When submitting annual report find Shareholders section and click on "change" one the line after your name.
Now enter new shareholder data including your correct place of residence. That is it.