It sounds pretty good to me. I would perhaps write the sound as "jse-m Matěj". The speaker is trying to distinctly separate the two consecutive "m"s. Perhaps that's what you're hearing?
Hi, I'm just wondering, why it appears as" ja jsem matej" for yes i am matej, but when it comes to no, it becomes " ne, matej jsem ja."
Are they interchangeable? Or negative so it reversed the position?
Just to expand (or confuse?) the answer further, both word orders can actually be used and it really depends on the intended emphasis and contextual meaning.
"Ne, Matěj jsem já." and "Ne, já jsem Matěj." are both valid, but the emphasis is different.
In the first sentence, the emphasis is on "já". In the second sentence, the emphasis is probably on "Matěj", although you could put it on "já" with intonation to get the same contextual meaning as the first sentence.
The emphasis on "já" would give you the sense that Balaovic described. The emphasis on "Matěj" could be used e.g if somebody asked if you are Jakub.
There are no reversed positions in negative sentences, it's meaning that's different: Compare: A- Kdo jsi? (Who are you?) B- Já jsem Matěj. (I am Matěj.) ---> question- you don't know the answer
A- On je Matěj? (He is Matěj?) B- Ne, Matěj jsem já! (No, I am Matěj!) ----> question- you think, you know the answer but wanna be sure ---->answer- "No, he's NOT Matěj, I am Matěj, I am Matěj- so please, REMEMBER IT!!!"
Yes, and because there are so many variations of every name, there is a simple rule in all the lessons of this course:
Do not translate the names, keep them as they are. You can omit the diacritics if you have to.
Allowing all the variants would be unmanageable.