Trademark A Logo
You should register both word trademarks and logo trademarks, since each protects different things.
With logo trademarks, you are not necessarily claiming exclusive rights to the literal words in the logo but are claiming rights to the look and feel of the logo as a whole.
Logo trademarks are not as strong as word trademarks (since they protect just the particular logo, and if you change the logo, you’ll need to file for a new trademark), but they can be easier to register.
When you trademark your logo, the “literal elements” of the logo (e.g. the words “law group” in our logo) are entered into the trademark database, where they can be searched/found by your competitors.
Since searches of the USPTO’s trademark database return both word trademarks and logo trademarks, both word trademarks and logo trademarks have deterrent effects (i.e. they discourage others from registering similar marks). So if you have a word mark that may be difficult to register because it is descriptive, then consider creating and registering a logo that includes the words.