What do you call the process of combining two words to create a new one?

In linguistics, a blend word is a word formed from parts of two or more other words. The process is called blending and the result is a blend word.

A portmanteau word typically combines both sounds and meanings, as in smog, coined by blending smoke and fog. More generally, it may refer to any term or phrase that combines two or more meanings, for instance, the term "wurly" when describing hair that is both wavy and curly.

The word "portmanteau" was first used in this context by Lewis Carroll in the book Through the Looking-Glass (1871).

I'm not entirely sure if there is a technical distinction between portmanteaus and blends or if the latter is a hypernym of the former. There is some suggestion that portmanteaux specifically combine the beginning of the first word and the ending of the second. But I've been unable to confirm the validity of this distinction and I've found that they're mostly used interchangeably. Any information on this matter is welcome.

P.S. ELU has tags for both these terms: portmanteau-words, blend-words.

I don't think there is a specific word for creating a portmanteau, but one usually coins new worlds, so the best expression would be coining portmanteaus.

The examples in the question are not compounds in the usual sense, since in each case one of the words is incomplete. I agree with SF that they are portmanteau words. ("Portmanteau" originally means "suitcase". It was common in England in Lewis Carroll's time. As Humpty Dumpty explains to Alice, "You see it's like a portmanteau—there are two meanings packed up into one word." See http://en.wikipedia.org/wiki/Portmanteau#Origin.)

• guesstimate: The coda of "guess" and the first syllable of "estimate" are pronounced the same, /εs/. In this word they are merged: pronounced only once (not "guess-estimate"), and the "ess" of "guess" is all that's written. You could say that those identical parts of the two words overlap in the portmanteau.
• chillax: The first syllable of "relax" is completely gone here: we just have "chill" + "-lax". The only overlap is the /l/, and again it is written as in the first word.