nicknames in japan?

I'm Matthew and when I talk to japanese people I tell them my name is matthew, but to be honest no one calls me Matthew, everyone calls me "Matt", but I tell japanese people my real name for no confusion, and I don't want to tell them my name is matt, so in japanese how can I say "I am matthew but my nickname is matt" and am I the only one? would this be considered weird or unusual?

what if I had a nickname not related to my real name, for example in High school my closest friends called me "Hiro" (they gave me a random japanese name just because I like anime).

in japanese how can I say "I am matthew but my nickname is matt"

Watashi no namae wa Mathew desu. Watashi no nickname wa Matt desu.

would this be considered weird or unusual?

Not at all.

what if I had a nickname not related to my real name

That's completely normal. But just as many English-speaking people may find it interesting that you have a nickname not related to your real name, many Japanese people may too.

isn't nickname "あだな" and the first "watashi no namae" this will be implied wounldn't it?

"Matthew desu, watashi no adana Matt desu"

Is this correct?

If your goal is to avoid confusion, just say your name is Matt. When people ask your name, most of the time they just want to know what to call you, not what is on your birth certificate.

If a situation comes up where I have to use my real name then they might think I lied to them.

I mean Matt, Sorry my keyboard is messed up, I thing you should just tell them what you said.

ummm... I don't think you your keyboard is messed up be you just totally spoke as if you were me...

Kisukeyo/Matthew,

Please refrain from posting under multiple usernames on the same thread (e.g. sockpuppeting).

"Matthew desu, watashi no adana Matt desu"

It should be "Matthew desu. (Watashi no) adana wa Matt desu."

But "nickname" is just as common as "adana." In fact, I'm not sure if younger people use the word "adana" any more. Meanwhile I agree that you should just call yourself Matt and skip the Matthew part.

I'm Japanese and there is nothing wrong with introducing your nickname in first place.
Just say

"Hi I'm Matthew. Call me Matt."

=

"Hajime-mashi-te, Matthew Desu. Matt to yonde kudasai."