> SpaceX was just a nickname for Space Exploration Technologies Corp

It's slightly more than that: it's a legally recognized nickname for the actual entity, technically called a "Fictitious Business Name" (aka DBA, "doing business as") registered with the state.

> there is such a thing as Starlink Services LLC

One might register a bunch of shell companies in various jurisdictions, holding various assets and contracts during the course of business, for tax reasons, to limit the blast radius of liabilities and facilitate business (for example, retail gift cards, e.g. Amazon, are often issued by a separate legal entity.) I think there's a qualitative distinction there with what Berkshire Hathaway or perhaps Alphabet Inc. do with their separate businesses that are hands-off subsidiaries. It appears at the moment Starlink is very much intertwined with SpaceX and user contracts and the trademark are actually directly owned by SpaceX, so not sure what they are using that particular LLC for.

It's for users outside the USA