Does gpg's symmetric encryption keep information about the filename? If I encrypt a file with gpg -c file.zip, and change the filename. Is there any way I can restore the filename as I used as a password. or the name encrypted to?
Yes, gpg -c file.zip does encode the input file name in the encrypted packet.
The gpg man page documents a few relevant options:

--set-filename string
Use string as the name of file which is stored in messages.

This  overrides the default, which is to use the actual filename of the file being encrypted.

--use-embedded-filename
Try to create a file with a name as embedded in the data. This can be a dangerous option as it allows to overwrite files.

This defaults to no.