I’m also very new to japanese but from what I gathered each Kanji has two different types of readings: KUN reading and ON reading; both of which have their own fair share of history and context behind them. what matters is that ON reading is most of the times used when the kanji comes together with another one and KUN reading is mostly used when it comes alone or with hiragana. Even though this is more like a probability rather than a rule you could say it’s true about 80% percent of the time.
However this doesn’t mean each kanji only has two readings; it’s possible that one kanji has multiple on and kun readings. In cases with kun readings it’s not too hard to tell the readings apart based on context and the hiragana that comes with them but with ON readings it might get a bit tricky since there aren’t many hints as to which possible ON reading could be used. At the other hand it’s not completely hopeless either since most kanji with multiple ON reading have one that is used more commonly so it’s safe to always place your bet on the more common one and check later to make sure.
It might sound a bit complicated at first but once you get a more familiar with how the system works you’ll definitely start to get along with it.
Also the kanji reading system for names is completely different, I don’t know much about it but it’s not nearly as systematic as the other two readings. Apparently kanjis have a third type of reading named nanori which is specifically used with names(?🤷♂️). That also means there are multiple different ways to write the name of the same person in kanji(?).
Anyway If you ask me I’d say name spelling system shouldn’t technically be too important for a beginner who’s only starting to get familiar with kanji.
So for your examples; about the first one: sometimes even the established reading seems to change based on the ON reading of the kanji that comes with it (convenience?).in this case the original KUN reading for 田 which seems to be た has changed to だ which might be because of the “n” sound that comes before. Why is the kun reading used even though the word is written completely by kanji? I don’t know either but as I mentioned the rules with ON and KUN aren’t that strict. A good example of established reading changing because of their accompanying kanji is the word 立派、(りっぱ) -meaning elegant- which is made up of 立 that has りつ as one of its most used ON reading and 派 which only has a single ON reading and that’s は. In this case you could say that since it’s not easy to put stress on the sound of は they changed it to ぱ Instead.
Your second example: I think 田中 is a name(?) so you probably shouldn’t pay too much attention to it; but you can see here that the original ON reading for 田 and the KUN reading for 中 (なか) are used here. Again why a KUN reading and an ON reading? I don’t know but since this is name we should probably be happy it’s not pronounced something more unrelated and crazier.
In the third example the established ON reading for both kanjis are used except that the こくfor 国 has changed to ごく which is another rare case (I swear they don’t happen to often) of ON reading changing slightly probably because of their accompanying kanji.
Sorry if this was too long of an explanation and also sorry I wasn’t good at explaining and also good luck with everything specially with kanjis and their reading😑