Google will only ever return sitelinks when it is absolutely 100% sure that the search user wants your site and no other site. If your site name only contains dictionary words or phrases used lots elsewhere online then Google will never 100% sure and will not return the site links for that search term.
Example of site names with no chance, little or some chance of sitelinks:
An example of this would be 'webdesign.com', the chances of sitelinks for the search term 'webdesign' is literally slim to no chance. If you were to have another domain called
webdesign247.com you chances increase, but not entirely because there will be other sites using 'Web Design 24/7' in their titles and descriptions, and Google may assume the user wants a web designer that is 24/7 and not a company called Web Design 247.
Unique brands trump Keyword Rich Domains
Branding trumps, having keywords in the domain name may appear to rank better at first but in the long wrong, you run into problems such as this one. You would not be posting this if you had the site name DingPingDonDon.
My website is BYBE.net and when I Google Search BYBE... I don't get sitelinks, here's why!
- Google assumes people might mean a BABY or the sounds that one makes.
- Lots of websites and YouTube videos are competing for the same term.
- I haven't worked on my BRANDING enough.
You can encourage site links on keyword based domains by working on your authority, but... if you have had a domain/site name that contains common searches, then your barking at the wrong tree, the issue is with the name of the site and not with Google and if this is very important then you should brand your site.