What does the name London mean?

Your friend is wrong on pretty much every point.

Donegal comes from Irish Gaelic, and means "FORT (not hill) of the foreigners."  The "don" part is actually "dun" in Gaelic.

London's name doesn't come from any local language, so a superficial similarity to an Irish word (which the locals didn't speak) is beyond irrelevant.  London's name comes from the Latin "Londinium" which is the name the Romans gave it when they founded it.

It's certainly possible that the Romans used a local name as the source for their Latinized version.  But that local name would have been Brittonic (or Brythonic) Celtic, not Irish Gaelic.

There is no evidence that "don" means "hill", but anyone who's walked all over London can confirm that although there are no steep hills, there are places where you are definitely walking up rather than along - from the top end of Whitehall up through Trafalgar Square and north to Shaftesbury Avenue is a definite slope. I know because I used to walk it twice a day for years.

. This from Wikipedia- "The etymology of the name is uncertain. There is a long history of mythicising etymologies, such as the twelfth-century Historia Regum Britanniae asserting that the city's name is derived from the name of King Lud who once controlled the city. However, in recent times a series of alternative theories have also been proposed. As of 2017, the trend in scholarly publications supports derivation from a Brittonic form *Londonjon, which would itself have been of Celtic origin"

It means Fortress. You can look it up.

London was named from the Latin word Londinium. It was changed to London after the Romans left the country.

The place name, recorded by the Roman historian Tacitus in the Latinized form Londinium, is obscure in origin and meaning, but may be derived from pre-Celtic (Old European) roots with a meaning something like 'place at the navigable or unfordable river'. ...