Passing a table name to a stored procedure
As @Shaulinator stated in his answer; the only way to accomplish this is to use dynamic SQL.  

Having said that, I would caution against applying the dont-repeat-yourself mantra too heavily to database code where it doesn't necessarily belong.  I realize your question is about Sybase ASE (now SAP ASE); however since SQL Server and ASE share a very common language I would point you to the dynamic SQL "bible" by Erland Sommarskog, The Curse and Blessing of Dynamic SQL

I would recommend templating your permissions code, such that you do a search-and-replace on the object name whenever you add a new object.  Retain the modified template code in your version control system; most likely in the same place as the object code itself.