After this FAQ it’s adviced to also check Free Software Foundation’s GNU License FAQ.
1. If changes are made to GPLv2 or GPLv3 -licenced product, but it’s not distributed, does the source with changes need to be published?
No.
If the product is only used inside a company, the clauses concerning the distribution of licence are not applied and it’s source does’nt have to published. For this it doesn’t matter if the product has been changed or not.
2. If changes are made to GPLv2 or GPLv3 -licenced product and it’s then distributed to clients, to whom does the source with changes need to be published?
To those customers. It’s not necessary to publish it for everyone, eg. via Internet.
3. I offer open source -software as ASP-service via network connection. I have made changes to the software. Am I obliged to publish the software’s source?
Propably not. Most open source -licenses do not interpret this kind of use as distribution of the software and thus the clauses concerning the distribution are not applied. For example in GPL-licensed software the source doesn’t have to be published in ASP-service, if the software itself isn’t distributed to clients.
There are, however, some licenses that require you to publish the source even when offering a service via network, like the GNU Affero GPL.
4. Is it possible to rename an open source -software offered to clients? Ie. can I re-brand an open source -software and what do I have to take into account then?
Yes. However, the new version must still contain all the information about it’s origin, including copyright information and the original license.