When the founders of Orion Satellite Corp. looked skyward for a company name, they picked a constellation that is the namesake of a mythological hunter. "We wanted the hunter's image of aggressiveness, skill, and wilines," explains Christopher J. Vizas, executive vice-president of the Washington, D.C., company.

Those attributes are critical for Orion, which is pursuing an elusive quarry: a piece of the international satellite-telecommunications market. For 20 years, that business has been the virtual monopoly of International Telecommunications Satellite Organization (INTELSAT), a global cooperative whose 15-satellite system operates under a 109-nation agreement. Nearly one-quarter of INTELSAT is owned by the U.S. representative, Communications Satellite Corp.

Orion and a handful of other companies are challenging the monopoly with plans to establish transatlantic satellite links outside INTELSAT. Last November, President Reagan endorsed the idea of opening the market to newcomers, but he imposed restrictions that would insulate 85% of INTELSAT's revenues from competition. Newcomers like Orion will not be permitted to carry residential telephone calls or communications between companies.

Orion plans to spend $250 million on a system designed in part for such intracompany communications as voice, data, and video. The company would sell or lease the satellite capacity at what it projects to be a price lower than INTELSAT's.

Vizas worries that unforeseen regulatory snags could threaten Orion's chances to compete successfully -- no matter how much aggressiveness, skill, and wiliness it brings to the new opportunity. Some larger companies, including RCA Corp. and Western Union Corp., are poised to battle Orion in the satellite market in the months ahead. "Right now we have a lead," maintains Vizas, as he eyes his potential competitors warily. "In another six to eight months, things could be different."