What people actually use is a matter of personal taste and orthographical knowledge. German orthograph is notoriously difficult. So it is often not clear when people use a deviating form, whether this was a deliberate choice or just a mistake.

Some companies even use camle-case for their products, such as Deutsche Bahn, which spells its discount card "BahnCard". But it is always okay to follow the official guidelines of the Council for German Orthography. For example the German Wikipedia spells it "Bahncard", while the English spells it "BahnCard".

Officially greographical names that do not apply to people are spelled without hyphen ("Berner Oberland" vs. "Schweizergarde", or in street names: "Berliner Straße" vs. "Robert-Koch-Straße").

Of the examples, the spelling "Alnatura Kicher Erbsen" is pretty awful. "Kicher Erbsen" is not a compositum of nouns (as one should never write "Berner Ober Land" or "Schwarz Wald" or "Alpen Vor Land"). If you want to keep the spelling as a proper name, I would recommend to put it in quotation marks and indicate that the non-standard spelling is not a mistake by adding a "[sic]" or "[sic!]" behind it: "Alnatura Kicher Erbsen" [sic].

Official brandings like "Eberhard Karls Universität Tübingen" are problematic. I would personally recommend to normalize them and use hyphens, but this is more a matter of personal choice. I myself find it most of the time more disrupting to use non-standard spellings than to deviate from the branding, especially when it would otherwise lead to inconsistencies in the flow of words ("Studierende der Ruprecht-Karls-Universität Heidelberg und der Eberhard-Karls-Universität Tübingen traffen sich." vs. "Studierende der Ruprecht-Karls-Universität Heidelberg und der Eberhard Karls Universität Tübingen traffen sich.")[1]

A final word about "Lebens-Versicherungs-Gesellschaft". Here we have two problems: a) This are not three words on the same level. One would never write "Lebens-Versicherungsgesellschaft"; but "Lebensversicherungs-Gesellschaft" is perhaps better than "Lebens-Versicherungs-Gesellschaft", because it structures the word along its meaning. b) "Lebensversicherungs-Gesellschaft" is not a simple compositum, but a genitive construct, which uses a so-called "Fugen-s" (there are more such joint sounds in German). You typically would try to avoid hyphens after such joint letters, because this sounds themselves are hyphens of some sort. However, a hyphen is permissible if it significantly increases readability. "Lebensversicherungsgesellschaft" is more elgant, but obviously harder to read than "Lebensversicherungs-Gesellschaft". It is a matter of style which one to use, and also a matter of genre. In a novel "Lebensversicherungsgesellschaft" may be preferred, but in a business document "Lebensversicherungs-Gesellschaft". Typically, in short composita hyphens should be avoided after composita ("Lebenszeit" not "Lebens-Zeit", "Seitenzahl" not "Seiten-Zahl"), except in very special cases (one may prefer "Verkehrs-Chaos" over "Verkehrschaos", because the Fugen-s is hard to spot due to the sequence "...sch...").[2]

Edit (plus some minor corrections in the text above):

[1] I am here deliberately not following the current guidelines of the Council for German Orthography that states (my translation): "Compounds of proper names and nouns for naming schools, universities, businesses, companies and similar institutions are written as they are officially defined." -- https://grammis.ids-mannheim.de/rechtschreibung/6158 (in German).

[2] Cf. § 45 of the current guidelines of the Council for German Orthography (my translation): "A hyphen can be used to emphasise individual components, to structure confusing compositions, to avoid misunderstandings or when three identical letters coincide." -- https://grammis.ids-mannheim.de/rechtschreibung/6159#par45 (in German). However, the text of the guidelines does not provide an example with a fugen-s, but does not prohibit it either. I suspect that the experts on the committee themselves did not agree.