What to do when my conlang has a word that means something in one of my languages?

This is a bit subjective problem. As a Hungarian who knows English, I have the high ground when it comes to making up words, as I can mush the English and Hungarian words together with some outliers (usually Japanese-sounding words) and things I make up. However, first, let’s take a look at a composite I created with my WIP Swadesh list:

rén+kile = red feather = rékile/régile

Red Feather is a rare genetic mutation among tengu (based-off of Japanese mythology; anthro birds, six-limbed variant). Those who are born with this mutation have striking red plumage, yellow/golden beak and eyes, along with an unusual pointy crest, similar to that of a cockatiel. Rékile is often translated to phoenix in Common (British English). While the resemblance is hard to deny, rékile tengu don’t set themselves on fire, nor revert into younger forms.

Now, régi means old in Hungarian. And Ré is Hungarian for Ra, who just happened to be a god with a bird’s head and is associated with the Sun (which is a deadly laser). Rékile is still passable, but some words are so reified in my mind that even lookalikes carry unwanted connotations.

who? (“?” not) = námó (I keep hearing nani)
what? (“?” not) = názá (Názáreti Jézus)

dog = gadór (csador Oh no! or csahol I’d prefer to go with that one)

I know it sounds and is dumb, but I can’t concentrate when I look at my language and I can still see the anime references and Hungarian words in my mind. I don’t want to throw out Hungarian entirely, but I’m still afraid people will pick up these accidental collisions of my languages. How can I minimize the number of those collisions?