Both "Did you see my DP?" and "Have you seen my DP?" are correct for written as well as oral conversations.
But if you want to know the difference between Did and Have, then here it is:
Did you see is used only for the Past Indefinite/Simple Tense. (Like we used 'see' which is in simple tense with 'did'). It works for works for recent past till now.
Have you seen is used in the Present Perfect Tense. (Like we used 'seen' which is in present perfect tense with 'have'). It works for anything that still applies from any time till the present, thus emphasises on the present.
Did you see the new movie? (A movie once released can be seen any
time. So it can be past or present both.)
Have you seen the new episode? (A TV episode airs only on a particular
day, so it's something very close to present.)
But for DP it can be seen at any time and also recently (because people change their DP frequently)
Present Perfect only emphasises on the present. It doesn't change the
meaning. So, both are correct but have a very minute difference.
Here's a great video to clarify this confusion.