If you need the Module Title from within a module control (which will inherit from PortalModuleBase) you can simply use:

Dim Title As String = Me.ModuleConfiguration.ModuleTitle

If you need the Module Title of a different module (or need to obtain the Module Title from a provider, etc.) you can use the following:

Dim mc As New DotNetNuke.Entities.Modules.ModuleController
Dim mi As DotNetNuke.Entities.Modules.ModuleInfo = mc.GetModule(ModuleId, TabId)
Dim Title As String = mi.ModuleTitle

As a module having the same ModuleId can appear on more than one page (Tab), if it has been created by adding a copy of an existing module to a page or the module's AllTabs property has been set true, the GetModule method takes a TabId as well as a ModuleId for its parameters.  I haven't looked at the Modules and TabModules tables for a while or at the 'GetModule' stored proceedure, but seem to remember that it can be called with TabId = -1. In the case of the ModuleTitle, it should be the same across all pages anyway.