Al-Kabeer is a name of Allah what about Akbar? Can we say it's not a name of Allah if it's not found in the Quran or Sunnah or should we need to say I cannot affirm it because it's not found in Quran or Sunnah. In this situation can a Muslim deny this as name of Allah because it's not found in the Quran or Sunnah is it kufur? Because we know Allah has many names and We know few of them through Quran and Sunnah we don't know remaining.
Akbar (اكبر) is an attribute to Allah. It is not a noun.
Kabeer is from the name of allah But Akbar is not from the nameof al lah. As we cannot see it in asmaul husna
Akbar أكبر is an Arabic adjective meaning greater, bigger, larger, older ... than (in case of Allah it means greater than any of HIS creation), which is derived from the verb kabura كَبُرَ which may mean has become greater, to enlarge, to increase etc. (not to confound with كَبَّر which is the verb expressing the act of takbeer -saying Allahu Akbar- or the noun الكِبْر or the adjective كِبْر referring to arrogance or dignity according the context) and the noun al-Kabeer الكبير (the great, the large, the big etc.).
Note that kabeer كبير without the prefix "al"/"ال" is also an adjective meaning great. The same logic applies to al-Akbar الأكبر which would be a noun meaning the greater, the bigger the larger etc.
As an adjective can't be a noun it is not among the names of Allah and can't be considered as such.
Also note that you may speak of Allah as the greatest an call him in Arabic الأكبر (Al-Akbar), but for this your audience should understand what you are referring to as it is not common to refer to Allah by this word alone, but you may find it quoted beside other attributes and names of Allah in many books of scholars. The same would apply for the adjective as one can use it to describe Allah's attributes as is done in the Adhan and iqamah by saying:
الله أكبر Allahu Akbar!
See also in the wording of this dua'