The defunct Ciudad Real Airport, also marketed as "South Madrid Airport", is/was about 200 km (227km from the Puerta del Sol, the official distance) away from Madrid

It just fails to beat your 'Frankfurt' Hahn, but Lydd Airport is also called London Ashford Airport, even though it's 117 km from central London. Given usual traffic conditions, that's probably a longer drive with a car than from Hahn to Frankfurt.

It's a bit of a cheat, but Bozeman Yellowstone International Airport (BZN) is approximately 150 km from the geographic center of Yellowstone National Park. Of course, Yellowstone National Park is huge; the closest point in the park is "only" about 75 km away as the crow flies, while the farthest point is about 200 km away. The park headquarters are 96 km from BZN.

Similarly, as pointed out by @user71659, Fresno Yosemite International Airport (FAT) is approximately 105 km as the crow flies from Yosemite Village. This is perhaps a bit less of a cheat than the Yellowstone case, since while there is not a town called "Yellowstone" in Yellowstone National Park, there is a town called "Yosemite Village" in Yosemite. (This does stretch the definition of a "city", of course.)

Not going to win, but another that’s over 100km from the city with the same name is Stockholm Skavsta Airport which is 106km by road to the Stockholm city center.

The distance

According to Google Maps, the distance from Bangkok to U-Tapao is upward of 170 kilometres by road, as shown in the screenshot below. The direct distance, as pointed out in a statement by Eva Air (in the quote below, in bold) is about 140 kilometres.

The future

There are plans for U-tapao Rayong-Pattaya Airport to become Bangkok's third airport. According to The Blue Swan Daily:

The Royal Thai Navy, operator of Utapao Rayong-Pattaya International airport, recently unsealed tender bids for the USD9 billion redevelopment of the facility under the Thai Government’s Eastern Economic Corridor (EEC) scheme.

Its summary of the article lists:

Utapao will ultimately take its place as a ‘Bangkok’ airport, but one dedicated to tourists as it serves nearby Pattaya.

The past

It's not completely unprecedented for flights to Bangkok to head to U-Tapao. In 2008, when both of Bangkok's main airports were closed, some airlines chose to direct their flight there. From web.archive.org's capture of the Eva Air website (emphasis is mine):

Suvarnabhumi Airport in Bangkok is still closed, so EVA Air changes flight schedule to Bangkok and Europe. EVA Air temporarily take Utapao Airport for the operation for flights to and from and via Bangkok.

Utapao is located approximately 140 kilometres and south from Bangkok. However, facilities at Utapao are very basic and the airport is heavily congested, we apologise in advance for the inconvenience, but ask for your understanding that the airport at Utapao is originally designed for military purpose.

It wasn't just Eva Air that decided to move it's flights, it has, for some time, been Thailand's main airport. From Wikipedia:

With the temporary closure of Suvarnabhumi Airport and Don Mueang Airport in late November 2008 because they had been occupied by anti-government protestors, U-Tapao became for a time Thailand's main supplementary international gateway. Many airlines arranged special flights to and from U-Tapao to ferry international passengers stranded by the closure of the Suvarnabhumi Airport.

As you can imagine, this caused quite a few problems (from the same Wikipedia link):

As many as 100,000 passengers were stranded in Thailand until early December. Although its runway can accommodate large aircraft, U-Tapao's terminals are not designed to handle more than a few flights a day. Travellers were subject to many hardships, and as the security was not up-to-date, some US-bound flights were diverted to Japan and their passengers required to go through a supplementary security check before continuing.

Not going to win, but Manchester Boston Regional Airport is about 44 mi (71 km) from the center of Boston (approximate straight-line measurement using Google Maps).

Ryanair's "Oslo" airport (TORP Sandefjord) is 87 km (54 mi) from the center of Oslo.

In general, I'd expect Ryanair's destinations list to include lots of good candidate answers to this question.

Once upon a time, Penzance (SW England, IATA code PZE, although pretty much just an airstrip) briefly advertised itself as "London Penzance", despite being 306 miles (492km) from London.

I can't find a link, but it was poking fun at the likes of "London Luton" (56km), "London Stansted" (61km), which claim to be alternatives to London City (13km), Heathrow (24km) and Gatwick (45km).

Not going to beat the other answers, but I wanted to throw in Weeze Airport anyhow, as it was supposed to be named "Düsseldorf-Weeze", but a court blocked the name due to the distance of 60km (Wikipedia claims 83km, the distance on road) from Düsseldorf.

Ryanair still calls it Dusseldorf-Weeze, however - I almost fell for it some time ago.