Almost certainly not, and here is the honest read on what is likely happening.
Every accredited correctional facility in the United States is required to provide inmates with basic hygiene items. Soap, toothpaste, and similar essentials are not optional amenities. They are baseline requirements under correctional standards, and facilities that fail to provide them face serious legal exposure. Maryland Correctional Training Center in Hagerstown is a state facility operating under Maryland DOC oversight, which means it is subject to those standards and regularly reviewed for compliance.
What facilities typically provide is the bare minimum. Generic bar soap, basic toothpaste, a toothbrush. It is functional and nothing more. It gets the job done without any extras.
Here is the part worth saying directly. Inmates have a well-documented tendency to overstate the conditions of their confinement when talking to family on the outside, particularly to parents. It is not always malicious. Sometimes, it is genuine frustration with a difficult environment being expressed dramatically. But it is also a reliable pathway to getting money put on the books, which then gets spent on commissary upgrades like name brand soap, better toothpaste, deodorant, snacks, and anything else that makes daily life more comfortable than the institutional baseline.
That is a completely understandable thing to want. The commissary versions of these items are meaningfully better than what the facility hands out. But the framing of not being given anything is almost certainly an exaggeration designed to motivate action on your end.
Putting a modest amount on his books periodically is a reasonable and kind thing to do. Just go in with clear eyes about what is actually driving the ask.