In reply to Steve Perry:
Write to the Palace giving your name, the location of the climb, the date you climbed it and the name you have given it.
The Palace will write to you in due course and when you hear from them indicate your willingness to accept the honour bestowed on you (the Palace always check first to avoid the embarrassment of a public refusal)
When summoned, put on your best suit, attend at the Palace, shake hands with the Queen (don't forget to bow) and accept your MBE* for services to British Climbing.
* If you've given it a really nice name like Royal Flush ,the Laughing Corgi or Corbyn's Downfall you might even be awarded an OBE