I am looking to play a Witch in Pathfinder, but I want to play a male witch. Can I do that, and if I can does the name matter? I'd like to call him a Warlock—can I do that?
While witch and warlock are arguably the female and male version of the same trope, just like a sorceress and a sorcerer, Pathfinder is intended to be retrocompatible with D&D 3.x material and D&D 3.x already has an official base class called Warlock (and a different Witch as an exaple of homebrewing a base class).
While I'd suggest to keep referencing to your character as a Witch (or a male Witch, when it could cause confusion), that is just a label the system places on the collection of powers, the class, and thus would only be used when speaking out of character, maybe when explaining your build to someone else or when reminding your Dungeon Master where to look for rules for your hexes.
On the other hand, in the game's fiction, it's perfectly fine to be calling a male Witch "a warlock". The same could be true for all Sorcerers/ress, or even all arcanists, depending on what "a warlock" is perceived to be in the game world.
(For ease of reference, all classes names are written with a Capital Initial, all descriptive names are in italics)
In most cases, yes.
Let's break it down.
Can my character refer to himself as a Warlock during roleplaying encounters?
In real life, I write programs for a living. When asked what I do, I can answer a lot of ways: Programer, Systems Developer, Web Application Designer, Male Model, Professional Adventurer, etc. Some of these are more accurate than others.
Your character has the same flexibility: he can describe himself however he wants. Witch, Warlock, Wizard, Fighter, Rogue, Adventurer... Regardless of what it says on your character sheet, you can say whatever you want.
Will the world acknowledge my choice of being called a Warlock?
Probably (ask your DM).
Are there others who call themselves Warlocks in the game?
When Bob, Captain of the Guard, hears that you're a warlock, does he know you mean a male witch?
If a Zone of Truth were cast on you, and you were asked your class, would you be able to say Warlock, or would you be compelled to say Witch?
These are all situations that are under the control of the DM. You'll have to ask him, but in most cases the DM will be cool with it.
Will the other players call me a Warlock?
It doesn't matter.
The other players will call you whatever they want to call you. Some will be respectful, some won't. You can express your preference of being called a Warlock, but they're under no real obligation to comply.
Can I write Warlock on my character sheet?
Unless your group are real sticklers for record keeping, it probably doesn't matter. Your character sheet is primarily for your reference, so put what makes you happy on it (as long as you can accurately recall the important parts of your character).
If I'm talking to someone (online or in person), and they ask what class my character is, can I say Warlock?
Well, you can. And it might even work within your group. But no one else will know what the heck you're talking about. Just go with Witch, which everyone understands.
The real question is why not? If the GM has an issue with such a small stipulation then frankly he should lighten up on being a control freak, especially over such a small matter. Why wouldn't you be able to do things like "translate" the class for a male character. It's the model of your character, it's what engages you. Of course again this ultimately falls to the GM but unless they are absolute about the guides of the role play this shouldn't be a problem.
Of course. Different cultures have different names for things, and while your definition of a Warlock might not meet up with what someone else considers a Warlock, doesn't mean your opinion is any different.
It's the same as mages/sorcerers/clerics/druids being called Witches and the like in less magically inclined lands with less formal understanding of the intracises of magic.
On your character sheet, yes, you're a witch, but you can introduce yourself however you wish, though it may lead to all sorts of in-character problems from people who expect one thing and you are another due to having differing opinions of what a witch/warlock/wizard/mage/sorcerer/arcanist/bard/etc is.