Yes. If your admission letter identifies me as your adviser it's because I have expressed willingness and commitment to support you. You may decide during your first year that another adviser is a better fit to your interests and if so that's perfectly fine, all you need is for that other adviser to agree to commit to you. It gets a little more complicated after the first year because by then you should really be engaged in PhD research and preparing for your qualifying exam - it can be done, it's just more difficult. Another possibility is to have another professor as co-adviser - I have had a number of students co-advised with colleagues. A danger is that you can fall through the cracks, as both your co-advisers may think that the other is supervising you and as a result you get no attention. But as long as you take initiative to avoid this the co-advising arrangement can work very well.