Adam אָדָם was generally held to be related to adom אדום. But adom means "red", not "dominion".
I have no idea whether this has been disputed since, as my knowledge here comes from religious and magical writers rather than linguists, and frankly religious and magical thinkers are very bad at etymology; creating links where there are none, and adding meaning where there are mere links. (At least it's better than the guy who argued angle the astrological term was cognate with angel).
Still, adom אדום (red) > adama אדמה (red arable earth) > Adam אָדָם at least was a traditional etymology, whether modern thinking agrees or no.
Jumping from adom to dominion makes no more sense than linking it to the West African name Adom. Less really, as it's easier to see how a name from the Abrahamic religions could influence another name.
The association between Adam and dominion is of course Genesis:
And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. So God created man in his image, in the image of God created he him; male and female created he them. And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth. (Genesis 1:26-28 KJV).
The Hebrew here is
וַיֹּ֣אמֶר אֱלֹהִ֔ים נַֽעֲשֶׂ֥ה אָדָ֛ם בְּצַלְמֵ֖נוּ כִּדְמוּתֵ֑נוּ וְיִרְדּוּ֩ בִדְגַ֨ת הַיָּ֜ם וּבְעֹ֣וף הַשָּׁמַ֗יִם וּבַבְּהֵמָה֙ וּבְכָל־ הָאָ֔רֶץ וּבְכָל־ הָרֶ֖מֶשׂ הָֽרֹמֵ֥שׂ עַל־ הָאָֽרֶץ׃ וַיִּבְרָ֨א אֱלֹהִ֤ים אֶת־ הָֽאָדָם֙ בְּצַלְמֹ֔ו בְּצֶ֥לֶם אֱלֹהִ֖ים בָּרָ֣א אֹתֹ֑ו זָכָ֥ר וּנְקֵבָ֖ה בָּרָ֥א אֹתָֽם׃ וַיְבָ֣רֶךְ אֹתָם֮ אֱלֹהִים֒ וַיֹּ֨אמֶר לָהֶ֜ם אֱלֹהִ֗ים פְּר֥וּ וּרְב֛וּ וּמִלְא֥וּ אֶת־ הָאָ֖רֶץ וְכִבְשֻׁ֑הָ וּרְד֞וּ בִּדְגַ֤ת הַיָּם֙ וּבְעֹ֣וף הַשָּׁמַ֔יִם וּבְכָל־ חַיָּ֖ה הָֽרֹמֶ֥שֶׂת עַל־ הָאָֽרֶץ׃
Which the dictionary tells me are forms from רָדָה (radah) meaning "rule" though with a variety of different connotations, suggesting "dominion" may be too harsh a nuance, or may not, as one chooses to interpret it. Either way, it's got nothing to do with אָדָם and nothing to do with dominium ("to own") from which we get dominion ("to own and rule" [from domus (home), cognate domestic]) beyond that being a possible translation.