Copyright in Design Work
Copyright protects design work where it constitutes an original intellectual creation under the Austrian Copyright Act. The author is always the person who created the work, and copyright itself cannot be transferred during their lifetime, so a company only ever acquires rights of use.
In practice
This is where many SME contracts are imprecise: "all rights pass to the client" comes to nothing under Austrian law, because copyright as such cannot be transferred; at best the clause is construed as a far-reaching grant of usage rights, at worst you end up arguing about it. Instead, expressly agree an exclusive right of use, unlimited in time and territory, including the right to modify the work and to pass it to third parties, otherwise you may be unable to have another agency develop your own logo further. Also clarify whether the agency may show the work as a reference and whether open source files form part of the delivery. Note that fonts, stock images and icons contained in the work carry their own licences, which do not transfer automatically. Whether a particular design reaches the required level of individuality at all is arguable case by case, and simple logos often do not reach it. That is precisely why contractually clean usage rights matter more than the copyright question. Settle this before the project starts, as licensing after the fact is regularly more expensive.