Should I capitalize the acronym of a word?

What you are trying to do is write an acronym (german wikipedia article). When writing a german acronym like you are doing here you normally capitalize only the first letter. It's called a Silbenwort (syllable word). Look at this example from the linked Wikipedia article:

Haribo für Hans Riegel aus Bonn
(Translation)
Haribo stands for Hans Riegel from Bonn

Another option is to use only the first letter and capitalize everything. Look at LASER:

LASER für Light Amplification by Stimulated Emission of Radiation

Your example is close to the first one, which means it should be:

Hosch für Hans-Otto Schwarze

Note that for example BAföG stands for Bundesausbildungsförderungsgesetz (law to support training/education) though. Here you can see that people were trying to denote the different nouns that are part of the composite word (Bund, Ausbildungsförderung (they could have split it into Ausbildung and Förderung and make the f uppercase, too, but that would slightly change the meaning as it's specifically the training that is supported), Gesetz). That means that if you have a single long word you have more leeway when it comes to writing uppercase and lowercase.

Note that companies can choose to write their name differently in their logo. Look for example at the Wikipedia article from Haribo (again in German). It shows the logo, which seems to be all uppercase, but the text mentions the name with only the first letter capitalized. When looking at the bottom of their website you will see everything capitalized again. The same is true for Hosch. I can't find a Wikipedia article on them and I don't know the company, so I would say writing their name should be similar to Haribo - meaning that only the first letter is capitalized, even if the Logo seems to suggest that every letter should be capitalized.