CurrentDocument.Parent is a TreeNode, so it has all the standard TreeNode properties, including NodeAliasPath.
Depending on your Kentico version, if you're needing some other page, I recommend DocumentHelper. DocumentHelper.GetDocuments() has a large set of methods for finding the pages you want - Column-level WhereEquals/etc filters, Type filters, Published(), etc. You're basically building a SQL query using the ObjectQuery syntax. Once you do that, use .TypedResult to get the InfoDataSet of TreeNodes you want. If you only want the NodeAliasPath, add .Columns("NodeAliasPath"), otherwise specify all the columns you want (or don't use a Columns() filter)
As far as DocumentNamePath, that's the tree-like list of Page Names of the parents, NodeAliasPath is the list of their individual page aliases, which are slightly different.