Should I obtain approvals to dissolve the small business set aside when I have solicited 4 small business vendors of a brand name product?
You are correct in that this is not full and open competition due to your brand name requirement (FAR 6.302-1(c)
Generally, unless you have an waiver from the non-manufacturer rule, then you can not do a set aside.
Also in FAR 19.502-2(c)
For small business set-asides other than for construction or services, any concern proposing to furnish a product that it did not itself manufacture must furnish the product of a small business manufacturer unless the SBA has granted either a waiver or exception to the nonmanufacturer rule (see 19.102
(f)). In industries where the SBA finds that there are no small business manufacturers, it may issue a waiver to the nonmanufacturer rule (see 19.102
(f)(4) and (5)). In addition, SBA has excepted procurements processed under simplified acquisition procedures (see Part 13), where the anticipated cost of the procurement will not exceed $25,000, from the nonmanufacturer rule. Waivers permit small businesses to provide any firm’s product. The exception permits small businesses to provide any domestic firm’s product. In both of these cases, the contracting officer’s determination in paragraph (b)(1) of this subsection or the decision not to set aside a procurement reserved for small business under paragraph (a) of this subsection will be based on the expectation of receiving offers from at least two responsible small businesses, including nonmanufacturers, offering the products of different concerns.
Based on this, then no small business set-aside is appropriate for your brand name sole source, even though you have small business distributors, you would only have one manufucter's product since it is a brand name requirement.