If you file one application for logo, consisting of a word and design, you obtain protection for the word in this particular design. Such protection is used often, but it is not too strong, it does not cover the word and design separately.
This means that:
1) if somebody uses a similar word in a different design, you will not be able to stop him, your scope of protection will not spread over such cases. And this could really prove to be a problem and mean loss of income or even deterioration of your own mark.
2) The same is true for the case when somebody uses a very similar design with a different word. You cannot file an appeal, because the word is different and the mark will be considered different.
Of course, if you can prove that the consumer could easily confuse your mark with that of the infringer, this would help, but it is difficult to do when only one aspect - the word or the design - of the infringer's mark is similar (not exactly the same), and the other is different.
So, much more strong protection is to file two applications: one for the word mark only in standard script with actually no design, and the other for the logo covering the word and design.
In this case, if an infringer uses a similar or identical word in any design, you will have the right to stop him and/or demand compensation because registration of a word mark covers the use of the identical and similar word in any design.
And use of the word mark is extremely helpful since, for example, name of a firm or a product is comprehended and remembered in linguistic form, it is reproduced in this way in mass media also.
If somebody uses a similar design with a different word, you could try to prove that the mark as a whole is similar to your mark. On the whole, registered should be the designation the producer actually uses; if you actually use the logo, it should be registered.
So, it is better register both the word and the logo by separate applications, if you are concerned about strong protection for the design and the word separately.