In most jurisdictions in Canada, being the "first" to climb a peak, reach a lake, etc. does not confer the right to name it. Of course, you are free to call anything whatever name you want, but that doesn't make it official.
1. convince the naming authorities that it NEEDS a name.
2. convince them that the name is appropriate for the feature
3. demonstrate that you've done due diligence to show that there are no pre-existing names for it, and no aboriginal names
4. get widespread support from clubs, aboriginal groups, local inhabitants, etc.