While we were the only publications publishing press releases when we started in 1997, it is common practice now.
And, all of those who do should be crediting a source at the bottom of the press release. Obviously, you want that source to be credited properly. And, you would never want to ask numerous media outlets to take their time to correct the source when they have been so kind to publish a bunch of your press releases.
So, at the bottom of the press release, just add this line:
SOURCE: [Insert Company Name]
Make sure you place it directly after the press release copy ends. Don’t have contact information or anything else before it. If a publication is copying the press release, they don’t want to have to remove extraneous information.