If my logo includes text, is the text also protected by the trademark?

When filing a logo, the text elements of the logo are partially protected, yes. All dominant and distinctive elements of the mark are implicitly protected, including text that forms a significant part of the overall impression. However, the level of protection is not equal to a registered wordmark.

Furthermore, the extent of protection depends on how distinctive the text element is on its own. In other words, if the text in your logo is your brand name and it is sufficiently distinctive, a third party using the same name in a different visual style may still be considered to infringe. If the text is generic or descriptive, it contributes little to the mark's distinctiveness and carries limited independent protection.

For unambiguous protection of the name in any visual form, a separate wordmark registration is the reliable approach. A figurative mark that includes the name protects the two together; a wordmark protects the name independently.