I blame 4Kids for this move, but...I have two theories on why they pulled this stunt.

THEORY #1

4Kids didn’t want the guy to be named “Spirit” (what Yugi was calling him before the screencapped episode) for the entirety of the English dub.  The available canon alternatives at the time were Mou Hitori no Boku (other me),Namonaki Farao (nameless pharaoh, and Yami no Yugi (Dark Yugi).

• 4Kids probably thought “Other Me” wouldn’t translate well for English-speaking children.
• Someone might’ve forgotten that the Egyptian aspect of the show was NOT a secret and feared calling the guy “Pharaoh” was been a dead giveaway even though they’d start calling him that in later seasons.
• 4Kids saw “Yami no Yugi” (or shortened to Yami Yugi) and decided it was shorter, easier to say, and was a good stand-in.

THEORY #2

A royal screw-up from either the Japanese or American teams led to a misinterpretation, where 4kids thought “Yami Yugi” was the ACTUAL name instead of a placeholder for the real one.  No one caught on until later in the English dub where they stop calling him “Yami” altogether.