In most cases, use your existing company. A business with years of history, tax returns, and past performance generally presents better to government buyers than a brand-new entity, and some contracts require the company to show a track record.
You do not need a separate company for each service line. One registered company can claim multiple NAICS codes, each representing a capability area, and bid across all of them. Your company registration is essentially your legal identity; your NAICS codes and capability statement define what you offer the government.
If you want to present a service line under a different name than your main company suggests, a low-cost DBA under the existing entity is usually the better route than forming a new company, while keeping a separate capability statement and web presence for that line as it grows. Your mentor reviews your specific situation on your strategy call and advises which route fits.