Do you think other petty kingdoms had their own bastard names, which got replaced as they were annexed? Like, did they really call all ironborn bastards “Pyke” even when the Hoares were ruling? Why would the ancient kingdoms of Oldtown or the Arbor use Flowers, which was a little too much like their neighboring realms’ imagery(actually, it seems more Tyrell than Gardner; wouldn’t Hand or something similar make more sense for a Kingdom of the Reach)? Or coastal valemen & stony Dornish?

It’s possible, custom does change over time, but I don’t think so.

Flowers makes sense to me – flowers grow a lot all over the Reach, so why would the Hightowers or Redwynes have an issue with it, especially since as you say it’s not associated with the Gardeners. Also, why would the Gardeners want it associated with them – none of the bastard names are similar to the names of Great Houses past or present, after all. 

Pyke is a bit odd, but my No Prize explanation is that it was chosen for the fish and not for the island, since being named after the island A. would insult the residents of said island, and B. wouldn’t particularly appeal to residents of the other Iron Islands. Whereas there’s lots of fish in the sea, as it were. 

As for coastal Valemen, I’m fairly sure they’ve got lots of stones there too. Ditto, there’s probably sand up in the Red Mountains.