Please go through below and play around with it.

Formula to change date format

As per standard functionality, we cannot modify the Date field in such a format (to include the text value of Month such as Jan/January, Feb/February etc.). However, the same can be achieved by creating a custom formula field by following the steps given below:

Select the Data Type as Formula and click Next Give a Field Label and Field Name Select the Formula Return Type as Text and click Next

Type one of the sample formulas given below (as per your requirement), within the box and Click Next Establish the Field Level Security and click Next

Add the field to the Page Layouts as needed and click Save

Sample Formula 1: To show the Date in European Date Format

text(DAY( xxxxxxx )) +' '+ CASE( MONTH( xxxxxx ) , 1, "Jan", 2, "Feb", 3, "Mar", 4, "Apr", 5, "May", 6, "Jun", 7, "Jul", 8, "Aug", 9, "Sep", 10, "Oct", 11, "Nov", "Dec") +', '+ Text(YEAR( xxxxxxx ))

Result: If Date value in the date field is 5/7/2015, the result in this formula field would be 5 Jul, 2015

Sample Formula 2: To show the Date in American Date Format

CASE( MONTH( xxxxxxxx ) , 1, "January", 2, "February", 3, "March", 4, "April", 5, "May", 6, "June", 7, "July", 8, "August", 9, "September", 10, "October", 11, "November", "December") +' '+ text(DAY( xxxxxxx )) +', '+ Text(YEAR( xxxxxxx ))

Result: If Date value in the date field is 5/7/2015, the result in this formula field would be July 5, 2015​

NOTE: In both samples given above, replace the values, xxxxxxx with the required date field's API Name that you would like to be displayed in a different format. To replace xxxxxxx from the formula, simply click on Insert Field button and select the date field you want to insert. This will show the API name of the field which can be used to replace xxxxxxx. Similarly, if you want to include the text value of the day as well along with date, from the given field, you can use the following formula: CASE(MOD( CloseDate - DATE(1900, 1, 6), 7), 0, "Saturday", 1, "Sunday", 2,"Monday", 3, "Tuesday", 4, "Wednesday", 5, "Thursday", 6,"Friday","")+","+' '+ CASE( MONTH(CloseDate ) , 1, "January", 2, "February", 3, "March", 4, "April", 5, "May", 6, "June", 7, "July", 8, "August", 9, "September", 10, "October", 11, "November", "December") +' '+ text(DAY( CloseDate )) +', '+ Text(YEAR( CloseDate ))

Result: If Date value in the date field is 5/7/2015, the result in this formula field would be Sunday, July 5, 2015

Here is Link to Knowledge Article:
https://help.salesforce.com/apex/HTViewSolution?id=000123532&language=en_US

According to the help docs you will need your format to be:

DATEVALUE( "YYYY-MM-DD" )  

You can also convert text to a Date so you can use the string value with your other Date fields and formulas. You’ll want your text to be formatted as “YYYY-MM-DD”...

If you are only needing the year from the existing text then you can use the RIGHT function described here.

RIGHT(Date_Key__c, 4)