Is a phonosematic matching word domestic in origin?

I’m having a lot of difficulty understanding your question, but what I think you’re asking is: can a word be both onomatopoeic (or otherwise iconic in some way), and borrowed?

The lazy answer, which is in fact the default answer from what I can tell, is no: if a name is an onomatopoeia, then its form is non-arbitrary, and you don’t need to go to the country next door to make sense of it. Dogs in English go “woof woof”, and you don’t need to look at German or Russian to know that; you just need to listen to a dog. Same for “splash” or “bang” or “bleep”.

Except that this is not true. An onomatopoeic form is not completely arbitrary, but it is still somewhat arbitrary; that’s why dogs in Greek go ɣav ɣav and dogs in Korean go meong meong and dogs in English go arf arf and yip yip and bark bark. Add to that that onomatopoeic forms can often end up inflected, and the inflections are certainly arbitrary and rooted to a place.

And the partially-arbitrary form one language picks for its onomatopoeia can travel to another.

I had my own epiphany about this just this year. The Greek onomatopoeia for sneezing is apsu (cf. English a-tishoo).

The Turkish onomatopoeia, I learned on Quora, is hapşuu.

If you pronounce hapşuu in a language with no /h/ and no /ʃ/, you get apsu. That is not a coincidence. The Greek word is an onomatopoeia, but it is still borrowed from Turkish.