There can be problems both ways.

i.e.) If I tell you my name is Japanese, it won’t be clear which Kanji I use for my name.

or If you see my name written in Kanji, it won’t always be clear how to pronounce it.

There are MANY common names which most Japanese people know how to read when they see it. There are, of course, always exceptions. Some names have more than one reading and the normal reading is not always the one used for people’s names.

Kanji – (Normal Reading) – Actual Name
東雲 – （とううん） – しののめ
東海林 – (とうかいりん） – しょうじ
九十九 -（きゅうくうきゅう）- つくも
(these can be seen as family names in Japan)

当て字 – is more when parents choose a completely unrelated reading for their kid’s first name. In recent years, new parents have been adopting a trend of choosing kanji based on style, stroke count or meaning and associating readings or pronunciations which would not commonly be associated to said kanji.This makes it nearly impossible to know how to say one’s name simply from looking at the kanji and requires furigana or someone to tell you.

The only example I can come up with right now would be
月 – (つき) – ライト (yes, I know this is from Death Note, but it meant to serve as an example of what I am talking about)