In my experience, most medium or larger companies have specific conventions for what different title levels mean. They're not (supposed to be) just honorifics, but rather indicators of responsibility and expectation. A senior developer will be expected to work with less guidance, to give guidance and mentoring, and to work at a level that has higher impact across the projectcompany.
Are you working at that level? In that case, discuss with your manager; describe what you're doing, and ask for your title to be changed to reflect your performance.
Asking for the title first and then promising to live up to it is the wrong way around. If you happen to be at a company where the culture accepts this, then, the titles will be correspondingly devalued. If you work at a company where titles and promotions are taken seriously based on performance, then they often are seen as meaningful by others in the company who may not yet have worked with you first hand. This is, however, a double-edged sword: it may get you into engagements you wouldn't have been considered for otherwise, but you'll also be judged by a higher standard and expected to live up to your title.