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What does one have to know in order to be called a "Talmud Chochum"? Hypothetically speaking If one knew Tanach or Medresh Rabbah well or even all 4 parts of Shulchan Aruch relatively well, then is he a Talmud Chochum?

And if it's not about knowing, then what does one have to do in order to be called a Talmud Chochum? Do we say that there are different levels (so to speak) of what it means to be a Talmud Chochum?

The Talmud provides several such definitions for various contexts. In the context of conditional marriages we have:

Kiddushin 49b

ע"מ שאני תלמיד אין אומרים כשמעון בן עזאי וכשמעון בן זומא אלא כל ששואלין אותו בכ"מ דבר אחד בלימודו ואומרו ואפילו במסכתא דכלה על מנת שאני חכם אין אומרים כחכמי יבנה כר' עקיבא וחביריו אלא כל ששואלים אותו דבר חכמה בכל מקום ואומרה

‘On condition that I am a disciple [talmid],’ we do not say, such as
Simeon b. ‘Azzai and Simeon b. Zoma, but one who when asked a single question on his studies in
any place can answer it, even in the Tractate Kallah. ‘On condition that I am a Sage,’ we do not
say, like the Sages of Jabneh or like R. Akiba and his companions, but one who can be asked a
matter of wisdom in any place and he can answer it. (Soncino translation)

In another context (according to Tosafot, who qualifies for having their lost objects returned by recognizing the object) we find another standard:

Chullin 44b

אמר רב חסדא איזהו תלמיד חכם זה הרואה טרפה לעצמו

R. Hisda said: Who is a scholar? He who would declare his own animal trefah. (Soncino translation)

Still elsewhere, we find definitions for various other contexts:

Shabbat 114a

ואמר רבי יוחנן איזהו תלמיד חכם שממנין אותו פרנס על הציבור זה ששואלין אותו דבר הלכה בכל מקום ואומר ואפילו במסכת כלה ואמר רבי יוחנן איזהו תלמיד חכם שבני עירו מצווין לעשות לו מלאכתו זה שמניח חפצו ועוסק בחפצי שמים והני מילי למיטרח בריפתיה ואמר רבי יוחנן איזהו תלמיד חכם כל ששואלין אותו הלכה בכל מקום ואומרה למאי נפקא מינה למנוייה פרנס על הציבור אי בחדא מסכתא באתריה אי בכוליה תנויה בריש מתיבתא

R. Johanan also said: Who is the scholar to whom a lost article is returned on his recognition
thereof? That [scholar] who is particular to turn his shirt.> R. Johanan also said: Who is the
scholar that is appointed a leader of the community? He who when asked a matter of halachah in any
place can answer it, even in the Tractate Kallah. R. Johanan also said: Who is the scholar whose
work it is the duty of his townspeople to perform? He who abandons his own interest and engages
in religious affairs; yet that is only to provide his bread.
R. Johanan also said: Who is a scholar? He who is asked a halachah in any place and can state it,
In respect of what practical matter?-To appoint him a leader of the community: if [he is well versed
only] in one Tractate, [he can be appointed] in his own town; if in the whole [field of] learning, [he
can be appointed] as the head of an academy. (Soncino translation)