Editing your company details such as company identifiers is done via the profile page. This app is opened by clicking this icon → 

You can read about this app in more detail here.

Once on the profile page, scroll down until you find the "Company identifiers" section:

To start adding or editing these values, click the blue "Edit" button at the top right corner of the section. All fields can now be edited. When choosing an ID type, Tradeshift will offer some suggestions, but you are welcome to add your own if you do not find any suitable ones:

Once you have selected the ID type, simply enter the ID itself in the field next to it. Note that Tradeshift will notify you of any invalid country-specific IDs you have entered, for example GLNs: