On a Microsoft Windows system, you can obtain the current date using the date /t command (the /t option prevents the command from prompting for a change to the the date) or by using echo %date% to display the contents of the date environment variable. However, both of those display the date in the form DDD mm/dd/yyyy, if the system uses a U.S. date format for displaying dates, where DDD is the day of the week represented by a 3-character abbreviation, e.g., "Thu", mm is a two-digit representation of the month, e.g., "08" for August, dd is the day and yyyy is the year.

C:\>date /t
Thu 08/06/2015

C:\>echo %date%
Thu 08/06/2015

You can reformat the representation of the date that is stored in the %date% environment variable. E.g, if you wanted the date in the form yyyymmdd, you can use a command like the one below where a variable, YYYYMMDD is set to hold the reformatted date; the variable name can be anything you like, e.g., mydate, etc.

C:\>set YYYYMMDD=%DATE:~10,4%%DATE:~4,2%%DATE:~7,2%

C:\>echo %YYYYMMDD%
20150806

The substring arguments to extract the elements of the date string are in the format %variable:~startposition,numberofchars%, so if the "T" in Thursday in the string "Thu 08/06/2015" is at position 0, the 10th character is the "2" of 2015 and I want 4 characters, i.e., "2015", so %DATE:10,4% will give me those characters. Or you can also think of the first number as the numer of characters to be skipped, i.e., %variable:~num_chars_to_skip,numberofchars%. I can then append %DATE:~4,2% to get "08" for the month followed by %DATE:~7,2% to extract the day, i.e., "06" if the date is August 6, 2015 represented in the %DATE% variable as "Thu 08/06/2015". Reference with additional links

If your batch file may be used on systems in other countries, though, you may need to make adjustments for a different style of date display other than month/day/year if you are reformatting the date rather than just displaying it in whatever format is the default one for the system. If you issue a reg query command, you can see the default format for the system. E.g.:

C:\>reg query "HKCU\Control Panel\International" /v sShortDate

HKEY_CURRENT_USER\Control Panel\International
    sShortDate    REG_SZ    M/d/yyyy

In the above example, I can see the system is using the month/day/year format. The setting for the country can be seen with reg query "HKCU\Control Panel\International" /v sCountry, but that may not be some thing you have to concern yourself with if you know the systems are local ones using a default date representation.

For ways to get yesterday's date there are several Stack Overflow postings, including the one mentioned by DavidPostill:

How to get yesterday's date in batch file?

how to get yesterday's date in DOS

dos batch programming: howto get and display yesterday date

Slightly OT, but if you are able to use PowerShell instead of CMD.EXE, it all gets much easier, e.g. you can use the Get-Date expression and a UFormat specifier, as documented here, to do exactly what you want. Powershell also makes it easier to do sensible arithmetic on dates, eg it knows that the day before 1 Jan 2025 is not 0 Jan 2025.

PowerShell is standard on versions of Windows going back to at least Windows 7.

Examples (here, PS > is a prompt in the interactive PowerShell ISE window):

PS > $oldfile = "backup." + (get-date (get-date).addDays(-1) -UFormat "%Y%m%d")
PS > $newfile = "backup." + (get-date -UFormat "%Y%m%d")

PS > echo $oldfile
backup.20171027
PS > echo $newfile
backup.20171028