bekannt
well-known
Known by many people; famous or widely familiar.
Diese Schauspielerin ist auf der ganzen Welt bekannt.
This actress is well-known all over the world.

known
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well-known
Known by many people; famous or widely familiar.
Diese Schauspielerin ist auf der ganzen Welt bekannt.
This actress is well-known all over the world.

'Bekannt' (known) is the past participle of the verb 'kennen' (to know). This connection helps you understand the meaning: what is 'bekannt' (known) is something that you, or the public, already 'kennt' (knows).
Er ist ein international bekannter Künstler.
He is an internationally known artist.
To express that something seems familiar, the structure 'etwas kommt mir bekannt vor' (something seems familiar to me) is often used. The person is in the dative ('mir' (to me), 'dir' (to you), 'ihm' (to him)).
Dein Gesicht kommt mir irgendwie bekannt vor.
Your face seems somehow familiar to me.
When you want to say what someone or something is known for, you always use the preposition 'für' (for) followed by the accusative.
Diese Region ist für ihren guten Wein bekannt.
This region is known for its good wine.
The expression 'bekannt machen' (to announce/make known) is often used for official announcements. Typical objects are 'die Ergebnisse' (the results), 'den Termin' (the date/appointment), or 'die Gewinner' (the winners).
Das Unternehmen wird seine Quartalszahlen nächste Woche bekannt machen.
The company will announce its quarterly figures next week.
When formally introducing people, 'bekannt machen' (to introduce) follows a fixed pattern: 'jemanden (Akkusativ) mit jemandem (Dativ) bekannt machen' (to introduce someone (accusative) to someone (dative)).
Er machte mich mit seinem Chef bekannt.
He introduced me to his boss.
new
'neu' and 'bekannt' can be opposites when the question is whether you already know something. 'neu' then describes something that is unfamiliar or not yet familiar to a person. 'bekannt' means that you have already seen, heard, or experienced it. Learners may confuse the words because 'neu' can also mean that something has just been bought or made. In this comparison, however, it is not about the age of a thing, but about whether it is familiar to someone.

Der Weg zum Bahnhof ist mir schon lange bekannt.
The way to the train station has been familiar to me for a long time.
Die neue Aufgabe im Kurs ist für viele noch schwer zu verstehen.
The new assignment in the course is still difficult for many people to understand.