in a nutshell, my company relocated to Europe and there we have a Ukrainian cultural centre called "Obiimy". This word means 'hugs' in Ukrainian. and as far as we are aiming to attract English speaking audience to our centre, we'd like to explain this word right in the logo. now it sounds like "this is how we say 'hugs' in Ukraine". But I don't like this explanation ;))
I'd say something "This is what we call 'hugs' in Ukraine"
or “This is what 'hugs' is in Ukrainian” or "This is Ukrainian for 'hugs.'
can you tell me which option sounds better to you as a native and if none of them, so how would you say it?

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I like "Obiimy is Ukrainian for hugs". It's clear. It also mirrors the wording of a supermarket slogan in the UK, so I probably like it for that reason too

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Among those options, the first one (“this is how we say ‘hugs’ in Ukraine”) sounds most natural to me.

For words in a logo, you could consider shorter phrases too, like these: ‘hugs’ in Ukrainian; that’s ‘hugs’ in Ukrainian;  Ukrainian for ‘hugs.’

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Firstly, is it a plural noun OR is it a verb in the third person?

Other than that I think any of the examples are okay. You could use any of them. But personally I would say something like "Obiimy is the Ukrainian word for 'hugs'" or even "Obiimy is Ukrainian for 'hugs'"

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What makes you ignore the variant "embrace"?

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You could even just put (Hugs) in parenthesis or italics underneath, maybe with a Ukrainian flag