Does a state name approval mean I own the name nationwide?
No. State approval generally means the name satisfies that state's entity-naming requirements at the time of filing. It does not by itself create nationwide trademark rights or guarantee that use of the name will not conflict with another party's rights.
Swyft Filings provides business-name resources and performs name checks as part of its filing process. A state name check focuses on whether a proposed entity name can be accepted under that state's naming rules; it does not determine whether the name is clear from every trademark, branding, domain-name, or marketplace conflict.