This is a disputed text. There exists manuscript evidence that 'me' may not have been used by the original writer.Jesus said in John 14:14, KIT "If ever anything you should ask me in the name of me this I shall do." which simply means,'If you ask me anything in my name, I will do it.'
at John 14:14 'me' is omitted after 'ask' in the following trinitarian Bibles: KJV; NKJV; ASV; RSV; JB; NEB; REB; MLB; LB; AB; CBW; NLV; LITV; MKJV (Green); Darby; Webster's; and Young's.
However, there is no such dispute about John 16:23 where John wrote: "... whatever you ask the Father for, he will give you in my name." We should ask the Father (not the Son) in Jesus' name.
(John 15:16) YOU did not choose me, but I chose YOU, and I appointed YOU to go on and keep bearing fruit and that YOUR fruit should remain; in order that no matter what YOU ask the Father in my name he might give it to YOU.
(John 16:23) And in that day YOU will ask me no question at all. Most truly I say to YOU, If YOU ask the Father for anything he will give it to YOU in my name.