Is it inaccurate to call Methodists members of the United Methodist Church (their official name) because of the schism over LBGTQ acceptance?

Doubtful. They have to change and become more accepting, or go out of business.

Should the United States change its name?

Schisms are commonplace in religions since factionalism is unavoidable. And as with anything as unweildy as a massive cult, the superstition itself will lag behind societal trends.

If there’s an official split and one branch changes their name, then they’ll be called by that new name. Until then, they’re all Methodists.

Overall, the United Methodists are a fairly liberal denomination, as are all of the Mainline Protestant churches, including the Disciples of Christ, Presbyterian Church-USA, United Church of Christ, Episcopal, and .Evangelical Lutheran. No matter how they vote, nothing will change.

There will be room for Gay and Lesbian clergy and churches, as there has been at least since the 1970s.

Some of the Mainline churches have split from their denominations, including the North American Lutheran Church (NALC) and some Episcopal churches have joined other Anglican groups.

No, the United Methodist Church does not represent all Methodists.

The link provided isn’t really accurate. Here is a page from the UMC.org that explains that the United Methodist Church does not represent all Methodists
http://www.umc.org/what-we-believe/are-all-methodist-churches-part-of-the-united-methodist-church

So you are starting with a bad assumption and going from there.