What is a suitable Chinese name for a fictional company called "The Unity Group"?
Well, I would say that depends on the nuances in The Unity Group.

"Some of them are employees of a Corporation"

Assume Group means 'Group of Companies，corporate group', a kind of financial wizardry for holding more than one company as separate tax entities.

corporate group: 公司 集团 gōngsī jítuán

Unity? Maybe: 团结 tuánjié

团结 就是 力量 tuánjié jiùshì lìliáng = Unity is strength

But maybe you mean unity as 'the only, we brook no challengers'? Like here:

德国 统一 社会 党 déguó tǒngyī shèhuì dǎng Sozialistische Einheitspartei Deutschlands  (Socialist Unity Party of Germany 1949-1990)

Here, unity is 统一 tǒngyī This means 'united' but actually they meant: the only party

(I've split the words for your clarity. Normally, everything is written together.)

Choose one: 统一 公司 团结 tǒngyī gōngsī tuánjié or 团结 公司 集团 tuánjié gōngsī jítuán

团体 also means 'organized group, team, organization'

Then there is 单位 work unit and 组织 organize, organization

Maybe you better clarify how you mean 'The Unity Group'.