Best way to place a logo with a new merger company logo? Would placing it next to each other be confusing?
I think you really want a design answer but the UX answer is...
Users don't care that your company has merged. Pick one brand and stick to it so that it isn't confusing.
There are two aspects to this (at least).
Visually it depends on the layout of the page, on the two logos and how well they work with each other, etc. The comments above are right in that it's better discussed on GD.SE.
In terms of UX, I believe that placing the logos far away from each other would actually be more confusing. If you place both logos at the same corner, you can tell some sort of story by manipulating the relationship between them. If one is small and one is large, that sends a message - this is the primary owner, and that's the secondary owner, for whatever reasons - e.g. it's a specific branch of the primary owner, or a subsidiary or something of that kind. But if you display one logo at the top right and the other one at top left, it becomes much harder to establish a visual relationship between the two.
The company I currently work for has made many acquisitions but instead of trying to change all the branding that made the company worth acquiring in the first place we simply let the user know in the footer that this is now "a SolarWinds company" that can link back to the main company page.
Don't go out of your way to let users know that a company has "changed hands" because people don't really care about who is running what as long as you make their life easier.
In the case of a merger, I would do some testing to see which name is more recognizable (in a positive way of course) and then use that brand everywhere.
I had worked in projects with similar case and we solved it as @DaveAlger said: adding the original company logo in the header (left, center or right -up to you-) and in the footer we add the holding company logo (the new merge company).