Let's say I created a software that automates the creation of Joomla CMS templates (this is just an example, I'm not into that). I manage to buy the domain name joomlatemplate.com. Great. But what about the software name? I cannot name it just "Joomla Template" cause it's too generic and I won't be able to trademark it in the future, right? But from the SEO perspective it would be best to keep the phrase "Joomla Template" in the product name. Do you see any reason why I shouldn't name my product "Joomla Template Generator" (if "Joomla Template Builder" is already taken)? I can't think of anything better than that.
This is a great question I have been asking myself for years because in a competitive space it seems every name is already used and domain names are taken, so you are kind of forced to be very creative.
Descriptive names with keywords are GREAT for SEO and brand building because if your customers use your product name as the phrase they search with you will most likely land at #1 spot for the phrase. You absolutely have to be prepared to spend more energy on building up a brand name that doesn't resonate with your product. I believe when ideal names are taken using synonyms works (builder > generator > maker). Research keywords and play with auto-suggest phrases on Google search field to get an idea of what phrases people use to search for a solution. Do make sure nobody is using the exact phrase you plan to use for your product to describe their product, even if there is no trademark they have earlier "use of name in business" in case of a trademark dispute.
A couple tips:
1. Don't just check for domain name availability, check NameJet.com for soon expiring or recently released domains as you might be able to find a better domain there then one that was never registered. You might even get some SEO juice leftover.
2. Don't fixate on a perfect name or domain name because you can always rebrand your product and find/buy a better domain name later. You can redirect en entire site to new domain without any loss of SEO rankings (I just did that recently, worked fine).
Generic product names can work and, more importantly, you probably shouldn't spend too much time worrying about the name anyways.
What kind of names are there anyways? Here's a list, fresh off the top of my head:
After spending a little bit of time looking for the above examples, I noticed a few patterns. Brand names are often random, sometimes 'meaningful', but rarely 'generic'. Consider how the names GM or 3M are now kinda random, even given their provenance. Product names actually seem to be a pretty chaotic mixture of all three types with a generic descriptive portion mixed with 'random' (alpha-)numeric identifiers and semi-meaningful evocative words, e.g. ViewSonic PRO9000 Projector.
Having now written all of the above, I'm not sure there is any concise advice to be offered about naming arbitrary products. Success is possible with any kind of naming and you can always market the same product using different names (or even brands) so you shouldn't feel trapped with any name(s) you pick initially.
* I had a hard time finding random product names; "Nexus" for example could arguably be considered semi or quasi meaningful tho it's not obviously or directly meaningful in my opinion.