How do I detect the name of used VR headset?

How do I detect the name of used VR headset? For mixed reality - Get HMD Device Name returns Steam VR and I need to be more specific

The SteamVR plugin has a GetVersionString function which may return what you are looking for. Unfortunately it is not exposed via Blueprints, so you will have to write some code to make use of it.

FString FSteamVRHMD::GetVersionString() const
{
	if (VRSystem == nullptr)
	{
		return FString();
	}

	const FString Manufacturer = GetFStringTrackedDeviceProperty(VRSystem, vr::k_unTrackedDeviceIndex_Hmd, vr::Prop_ManufacturerName_String);
	const FString Model = GetFStringTrackedDeviceProperty(VRSystem, vr::k_unTrackedDeviceIndex_Hmd, vr::Prop_ModelNumber_String);
	const FString Serial = GetFStringTrackedDeviceProperty(VRSystem, vr::k_unTrackedDeviceIndex_Hmd, vr::Prop_SerialNumber_String);
	const FString DriverId = GetFStringTrackedDeviceProperty(VRSystem, vr::k_unTrackedDeviceIndex_Hmd, vr::Prop_TrackingSystemName_String);
	const FString DriverVersion = GetFStringTrackedDeviceProperty(VRSystem, vr::k_unTrackedDeviceIndex_Hmd, vr::Prop_DriverVersion_String);

	return FString::Printf(TEXT("%s, Driver: %s, Serial: %s, HMD Device: %s %s, Driver version: %s"), *FEngineVersion::Current().ToString(), *DriverId, *Serial, *Manufacturer, *Model, *DriverVersion);
}

How about WindowsMixedReality for SteamVR, will it still work?

Sorry no idea about that. You can try asking on the forum here:
https://forums.unrealengine.com/development-discussion/vr-ar-development
Some people are experimenting with it.

WMR does not work for unreal, every build has a terrible flaw that stops it from being practical.