What single term or expression is used to rename a type of name for an object?

Question

I am seeking guidance on alternate words or grammatical rule for renaming a type of name that an object might have. As an example you might refer to you cell phone with a number of different types of name. Model name (i-Phone 6), Family name (Apple i-phone), pet name (Apple phone the destroyer), common name (i-Phone, Phone, etc) etc.

If I were to change the     Would I say         As opposed to
-----------------------     -----------         -------------
short name                  reshort name        change the short name
reference name              re-reference name   alter the reference name
local name                  re local name       modify the local name

So to change a name of a mountain is to rename the mountain.

To change the short name of a mountain is to "what?" the mountain?

What is your suggestion for an alternate word or grammatical structure?

Answer 1

Change can be used for all of them. Change the short term, change the reference name and change the local name. Alter and modify could be misleading or have another meaning.... or Use another short term, use another reference name or use another local name.

rename an object, by changing its name. rename an object by replacing its name with another.

Answer 2

Edit would be a one-word term for making slight or complete changes to most anything.