hi
not just "no", but [REDACTED] no
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Let's be slightly more serious, though.
The other States of the Union that got themselves split into multiple states of the same name were split on more or less an even basis. The Province of Carolina was huge and unwieldy and impossible for the colonial government to manage effectively and so got itself split into more or less coequal chunks. The Dakota Territory also got itself split into basically coequal chunks.
What became West Virginia in 1863 was not more-or-less half of Virginia. It was always the "different" part - different terrain, different population numbers, different population type and density, vastly different history, and so on. Most of what became WV was west of the Proclamation of 1763 line, and thus didn't really participate in Virginian colonial history until very late in the game. It remained the "different" part of the state long after the Revolution. Ideally, this would have been reflected by a name appropriate to its status as "not really Virginia", just like how Vermont was named, well, Vermont rather than rejoicing in the horrifically absurd mouthful of Northeast New York. And so, when the Unionist counties of western Virginia aggregated under federal military protection in 1861, they first organized under the name of the State of Kanawha, an exceedingly appropriate name due to the prominence of the Kanawha River in western Virginian geography. (It would also have made for a good litmus test to see who's from the state and who isn't; to this day, well over 99% of people from outside WV cannot correctly pronounce "Kanawha".)
Unfortunately, the 44 idiot delegates to the state's first constitutional convention in December 1861 abandoned the name of Kanawha and settled on West Virginia, explicitly to acknowledge the new state's heritage as formerly being part of Virginia. The new name is brainless in most respects, but it does get one thing right: West Virginia is basically, in Virginians' eyes, the crappy offshoot of Real (tm) Virginia. They may very well have been politely hoping for a rename! But it ain't gonna happen unless something apocalyptic changes.
The most important reason, in most Virginians' eyes, is that their state has all the history and WV's doesn't, and changing the name would be like abandoning that history. Related to that reason is the second reason, which is that populous and wealthy Virginia is not going to change its name just because thirty men in Charleston in 1861 decided they wanted the hick part of the Commonwealth to have a different name. West and East Virginia implies some sort of coequality. West Virginia is clearly inferior in the real world - say the Virginians - in basically every way and therefore "proper" Virginia ought not stoop to their level. Now, sure, you could happily argue that Virginia lost any right to its old name by rebelling, and frankly I would agree, but the fact of the matter is that nothing was done about it back in the 1860s when it might have actually made sense and changing it now would be absolutely bonkers, especially since nowadays Virginia is way more Unionist than West Virginia is.
There's also the geographic argument. "East" Virginia extends further west than does West Virginia, due to Lee, Wise, and Scott Counties. North and South Virginia would be slightly more accurate, because the northernmost point of WV in Hancock County is way further north than Loudoun and Frederick Counties in VA while the southernmost point in VA (too many counties to name) is south of the southernmost point in WV. But it would still never ever happen. Also, anyone who seriously touts Northwest and Southeast is just kidding himself.
For what it's worth, West Virginia has a long history of flirting with cool names (like Vandalia) and appropriate ones (like Appalachia) but ultimately settling on terrible ones (like Westsylvania). Frankly, at this point, they thoroughly deserve their terrible name even if it confuses geographically illiterate foreigners.
