Based on the Web Content Accessibility Guidelines (WCAG), a company logo with a text alternative meets accessibility requirements.
Logos and logotypes are not included in Success Criterion 1.4.5 Images of Text, since their visual presentation is considered essential. Logos also do not need to meet the requirements of Success Criterion 1.4.3 Contrast (Minimum) ("Text that is part of a logo or brand name has no contrast requirement"). However, if you have flexibility with the logo design and can make it pass contrast guidelines, that's a great thing to do.
All other text must meet the minimum contrast ratios. So you'll need to adjust the colors being used for text and backgrounds so that they meet the requirements. For WCAG 2.1 AA, it is required that normal text has a ratio of at least 4.5:1 and 3:1 for large text. AAA requires 7:1 for normal text and 4.5:1 for large text. Take a look at our Q&A for techniques on how-to check contrast ratios.