When mysqldump is created with --databases or --all-databases option, it will add "CREATE TABLE" and "USE" statements. If you need to restore the dump into different database (different name) you need to remove those statements. For small files it's not a problem - just edit the dump with your favourite text editor. However huge MySQL dumps (e.g. gigabytes big) may be a challenge. Editing with vim means loading the wohle file into the memory - not a good idea.
Filter dump file with grep to ignore CREATE and USE lines on the fly, while restoring:
Edit the file by overwriting CREATE and USE lines with spaces (so file size will not change). In hexedit use TAB to switch to ASCII editing, F2 to save, F10 to exit.
Use mysqldump-filter PHP script to do the same as above.