From Sonic Retro

The arcade game, SegaSonic the Hedgehog, was originally referred to as just Sonic the Hedgehog. Its instruction card still refers to both names.

For a short period in Japan, the Sonic the Hedgehog series was referred to in merchandising as SegaSonic the Hedgehog (セガソニック・ザ・ヘッジホッグ). This moniker continued to be used until around 1994/1995, when the "Sega" was dropped (as was the case internationally).

"SegaSonic" is thought to have been Sega's solution to a trademark dispute, caused by Taito and its 1990 release of the arcade game, Sonic Blast Man. The details are sketchy, but it is believed that Sega could not use the "Sonic the Hedgehog" name as intended, leading to "SegaSonic the Hedgehog" being used in arcade games, merchandise and advertising. Sega does not appear to have compromised on the name until late 1991 - some earlier products from the time of the original Sega Mega Drive Sonic the Hedgehog release are unaffected.

Prominent video games affected by this dispute include the 1993 arcade game SegaSonic the Hedgehog, SegaSonic Cosmo Fighter and SegaSonic Popcorn Shop as well as and the unreleased SegaSonic Bros.. Games for the Mega Drive and Sega Game Gear were unaffected.

The dispute was likely resolved some years later, as the SegaSonic name has not been seen in new products since the 1990s.