When obtaining a word mark from the USPTO just isn’t possible, but you really want to keep your name, you can try for a logo mark, whereby your register your actual fully designed logo in all it’s colorful and shapely glory.
Stylized or design (logo) marks can be a way to differentiate a mark enough to avoid a potential conflict, but it depends on how predominant the design part is, and whether the conflicting marks are standard character marks or also designs. If the word characters predominate the logo and there is a conflicting standard character mark already registered, an examiner may not find the design is distinct enough to overcome a conflict (reasoning that a consumer will still focus on the words and may be confused). This is because when you register a standard character mark, it means you can present the mark in any format you like. However, if the only conflicting marks are stylized/designs, then yes, having your own stylized/design mark that looks different from such other design marks will help in registration.
The traditional advice is to try to obtain a standard character mark first for a new brand because you may not want to tie your brand to one logo too early in the brand lifecycle. Unless you are absolutely in love with your logo and have no intentions of changing it for many years, it's better to have the flexibility in marketing to present the mark in any format.