Is there a mental disorder in which one is unable to determine personal preferences, and as a result, is a cause of great distress? I know that our preferences and tastes help shape our behaviors and what activities we willingly engage in, but I also know that being faced with indecision is a common feature of the human experience. However, I wanted to know if there is a mental disorder classified in the DSM or elsewhere, where an individual's indecisiveness is so great that it prevents one from settling into an identity and determining what hobbies, interests, aesthetic preferences, etc. to pursue, and as such, causes a large amount of distress and significantly impacts said individual's life?
There is no specific symptom criteria in DSM that matches your description. It’s a very general problem that can be conceptualized in a variety of ways. 

The closest thing I can think of that resembles your description would be generalized anxiety disorder (GAD). Dugas and Ladoceur claims in their research that the main underlying factor causing GAD is intolerance for uncertainty (IU), which - among several things - increases anxiety in decision making. IU paired with another factor for GAD - cognitive avoidance - causes tendencies to avoid difficult decisions completely, or dealing with decisions with excessive worry. 

https://www.ncbi.nlm.nih.gov/m/pubmed/11142548/

Please bear in mind that proper assessment and diagnostic requires a face to face consultation with a licensed specialist.