Generally in fiction writing, you don't italicize company names (even though you would italicize the name of a newspaper).
But what do you do if the company name is fictional, especially a name that is not a real word (Like Schwaye). Italicizing it would make it clearer to the reader that it is a name (and not a typo). It would also make the name easier to read.
What happens if the text has a mix of fictional and real world company names (e.g. the BBC and Schwaye). It seems a bit odd to have a mix of italics and roman.
Example:
Alice would always go to Adam's restaurant.
[Couple of chapters later]
After leaving Adam's, Angela checked her email. She had got a message from Schway, the famous social network, which was even bigger than Facebook or Twitter.
versus:
Alice would always go to Adam's restaurant.
[Couple of chapters later]
After leaving Adam's, Angela checked her email. She had got a message from Schway, the famous social network, which was even bigger than Facebook or Twitter.
I'm not sure but I feel it might read easier with italics (especially Adam's)