Term for creating a fantasy word from all letters of two existing words?

Solution 1:

The National Puzzlers' League maintains a guide to wordplay terminology that has a few terms that might be useful. Some of these terms are commonly used, and others were coined by NPL members.

• transposal is any rearrangement of letters from a word or phrase to another word or phrase
• anagram, as defined by NPL, is a transposal where one arrangement forms a clue or description of the second arrangement. NPL imposes some additional rules for good anagrams; these are at the link.
• alternade would work, if your single word were formed by taking one letter at a time from each of the source words in order, e.g. HAT + ERS = HEARTS.
• rebade is a variation of the alternade that is also a rebus
• interlock is like an alternade, except the source words don't have to be the same length
• transade would work, if your single word were formed by transposing each of your source words separately and then appending them together, e.g. ASH + REV = SHAVER.
• alterposal is like an alternade where the source words are transposed first
• transinterlock is like an interlock where one of the the source words is transposed first

Given these definitions, the example you have given, LAMP + VAMPIRE = VAPAMLIMPER, is merely a transposal, and since it is a protologism rather than a neologism, I would call it a transposal protologism or a protologistic transposal.

You could combine your source words using the more restrictive rules for one of the specific transposals to make things more interesting. For example, LAMP + VAMPIRE = VAMLAPIMPRE would be a protologistic interlock. LAMP + VAMPIRE = VAMMAPPIREL would be a protologistic transinterlock.

Solution 2:

You can call it a blend word

In linguistics, a blend word or a blend is a word formed from parts of two or more other words. These parts are sometimes, but not always, morphemes.

It's also similar to a portmanteau, except that with a portmanteau, the beginning is from one word and the end from the other, rather than mixed up.