The purpose of dbDelta() is both to create and update tables. If you don’t need updates then you can skip it.
For keeping track of name you can simply follow WP convention and save name of your table in field of $wpdb object.
Also note that you should consider there is possibility of code running on multisite. Even if you are not releasing it you might need to run it that way one day and then you are in for a painful refactoring if all table-related stuff is hardcoded.