1) according to the business scope of your company, I suggest that Catering Operation Co, ltd. is better. 2) If your company is large, it is more appropriate to use your name, but it seems unnecessary to put trade in it. The company name had better be concise. 3）Food& Beverage generally refers to restaurant catering, which is a little different from your. 4)cater is a verb, which is used to express action and predicate in sentences. You are the company name here, and there is no action, so adding ing becomes a gerund, that is, the meaning of the verb is not the form and usage of the noun, which is more appropriate.