My question are we able to purchase this carpets with O&M money under the Governmnet Purchase Program, and what's the reference that would give us guidance for this purchases and support it or prohibited.
O&M funds should be appropriate for this purpose. Specifically, DoD Financial Management Regulation Volume 2A, Chapter 1, p. 1-17 states,
"Costs of facilities restoration and modernization projects, not financed by Military Construction appropriations, meeting the current criterion for funding from appropriations available for operation and maintenance are considered expenses."
Just because a unit logo is added does not change the basic nature and need for the carpets. Of course, good business sense in these times of fiscal constraint should be a consideration.
Consider checking DAU's ACQuipedia article on O&M funds
for further guidance.