Mapping probe ID to gene name
To end up with a single table made by merging all your tables, you can give a try with reduce() of purrr:  The first argument .x would be the list of tables to merge (in your case the annotation file plus all the other files) and the .y argument would be your function, i.e. inner_join(). reduce() would merge all the tables within the given list, left to right or right to left. ... would enable you to specify column(s) to use as "anchors" while merging.

If you would prefer to keep your tables separately then lapply() is the answer: lapply(list_of_files, function(x) inner_join(annotation_file, x)). This would give a list of merged tables.