You really do not want to arrange a cab with the hotel for a ride from the airport. There are so many cabs and ride services available from the airport. There is no reason to get a hotel involved and likely pay an extra cut. Not to mention if you are having to go through Immigration at DMK can add anywhere from five minutes to four hours to your pick-up time. Likely a hour but it is unpredictable.

If you turn left as you walk away from baggage claim but are still in the building and walk to the end of the airport, there will be lines for you to get a slip to get a cab. This is usually a very fast process. I cannot remember having to wait more than a minute. (DMK is not some third world airport like AOO where you are stuck 23 miles away from the city out in Martinsburg in some cornfield where there may be no cab.) If you want to call Uber that will work, too, just be sure you are clear on the pick-up point Uber will take a little longer. There are also car services that are more expensive. Some people like those.

The FT Thai travel forum has a thread that gives information for getting a taxi and one about DMK. Both are on the first page, towards the top.

Including the 50THB pickup fee a taxi should be about 330THB. (~$10.50 USD)