than is initially calculated

a) It should be was, not is, but yes, it can be omitted

b) the is incorrect. The article is only used as part of a proper noun in a few cases - generally if the noun has an adjectival component - eg the Netherlands, the United Nations. There are exceptions, but Athens isn't one of them

c) You've given no context for this sentence, but if it was eg a newspaper report, it would be more usual to include that than to omit it, as the style would be neutral rather than informal.

So the sentence should be :

He says that Athens will need more bailout money than was initially calculated.

or

He says that Athens will need more bailout money than initially calculated.

Excellent answer. Thank you.