Can anyone help me figure out these sitelinks?

[DanDeceuster]

My company is Squatty Potty (yes, of magic unicorn fame) and I recently redid our website's navigation. We're overhauling it currently to rebuild the whole thing, but what is there should give a good idea of site hierarchy to Google I would think.

The funny thing is, when you Google [squatty potty website] we do have sitelinks. But when you Google just [squatty potty] we don't. Any ideas on why sitelinks would appear on one search but not the other? I see they appear with [squatty potty logo] as well. I can't figure out how to get them to appear for my brand name search, any help appreciated!

[tosbourn]

For what it's worth, I'm seeing the opposite, see attached screenshots.

Searching from the UK.

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[emilslv]

Actually i have different results ...

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[DanDeceuster]

Oh, I'm actually only looking at U.S. results of our .com. International sites are controlled by other distributors.

[DanDeceuster]

So those sitelinks you see for [squatty potty website] are what I want showing up for [squatty potty] as well. I see a couple text links is all, not expanded full sitelinks.