At least some Starlink units have been paid by SpaceX.
It is not possible to establish whether any of those were "paid by Musk himself", no sources cite anything like that.
It seems that of total $15M / 5,000 units affair,
only USAID has paid circa $3M, including:
- $2.25M for 1,333 units at the price of $1,500/ea.
(cf. retail price $599, but it may or may not include subscription costs)
- $800k for delivery of all 5,000 units.
Also, "some help" from France and Poland was acknowledged.
Other sources claim that about 85% of the 20,000 terminals in Ukraine were fully or partially paid for by the US, Poland or other entities, which corroborates with the remaining 3,000-3,500 units.
The rest might have been paid by SpaceX, but its President Gwynne Shotwell has declined to provide with details.
This article has been published on The Washington Post on April/08/2022:
U.S. quietly paying millions to send Starlink terminals to Ukraine, contrary to SpaceX claims
It refers an article at USAID.gov site that initially was more specific about numbers, but allegedly has been revised since then.
Original post (Web Archive)

As it is today (link)

The WaPo article also says:
USAID spokesperson Rebecca Chalif told the Post that the “delivery of Starlink terminals were made possible by a range of stakeholders, whose combined contributions valued over $15 million and facilitated the procurement, international flights, on-the-ground transportation, and satellite Internet service of 5,000 Starlink terminals.”
Poland seems to have also paid for another lot of 9,000 units:
The largest single contributor of terminals, according to the newly obtained documents, is Poland with payment for almost 9,000 individual terminals. — CNN, October/14/2022.
The total number of units in Ukraine has reached 20,000, of which 85% (17,000) have been paid by others, so it leaves circa 3,000 units that could have been paid by SpaceX itself:
According to the SpaceX figures shared with the Pentagon, about 85% of the 20,000 terminals in Ukraine were paid – or partially paid – for by countries like the US and Poland or other entities. Those entities also paid for about 30% of the internet connectivity, which SpaceX says costs $4,500 each month per unit for the most advanced service. (Over the weekend, Musk tweeted there are around 25,000 terminals in Ukraine.) — CNN, October/14/2022.