What must the written record include regarding the sample collection?

The correct answer emphasizes the importance of detailed documentation in the sample collection process. The written record must include not only how the sample was collected but also any problems encountered during this process. This information is crucial for ensuring the integrity and reliability of the sample, which is vital for subsequent analysis or regulatory compliance.

Detailing the collection method provides transparency and allows for reproducibility in future sampling efforts. Moreover, documenting any problems encountered can help identify potential issues that could affect the sample's quality or the results of the analysis. Such thoroughness is essential in maintaining the credibility of environmental monitoring and remediation efforts, particularly concerning heating oil tanks.

The other options, while they touch on aspects of record-keeping, do not encapsulate the necessary scope of information that must be included in the context of proper sampling procedure documentation. Focusing solely on time, location, equipment used, or just the names of those involved would likely omit critical details that could impact the interpretation of the sample data.