You can always request. As to whether you can get it, that is another matter entirely.
For “toll-free” numbers (800, 877, 866, 855 “area codes”), there is an active market place for buying and selling.
For regular numbers, they are allocated/issued to local carriers as needed, generally in blocks of 10,000 – smaller blocks if the area code is almost full. If the current holder of the number gives it up (after possibly taking it with them through several moves to other phone companies), I believe it reverts back to the owner of the prefix. If you want that number, you have to talk to that carrier.
Usually, when you open a new service, they will give you a choice of 10–12 numbers. For years I had the number xxx-569–5277, which I spelled out as LOW-LARS. Most people found that easier to remember than 7 digits. When my daughter got her first cell phone, I picked xxx-xxx-KATP (for Katherine Poulsen) but she hated that. “I don’t want to be cat-pee! – Yuck”.