My tree is on Ancestry, and I follow the convention that they use, which is the woman is displayed with her original surname. You can easily tell who she was married to, even if it was multiple husbands, because the trees will show those relationships. Having the original surname shown for the woman, and having her in the tree next to her husband, is one of the few ways to connect the same woman pre- and post-marriage, particularly for women born prior to 1930 or so, for which there are few documents that will contain the first surname.
This is also one way to sort out the all-to-common question of "My grandfather Abe Gold had a sister Rose who came to the US in 1911, and then she disappeared. What happened to her?" Most likely, she got married. If people put her in their trees as Rose Gold, married to Harry Weiss, it will be a lot easier for others to find her. It will also be a lot easier to connect her to her siblings and parents.
It would be much more helpful, genealogy-wise, if we followed the convention that is used in Spanish-speaking countries, where the woman in official records is shown with both her original and married surnames. I have a relative Sarah Lavine who migrated from Russia to Cuba, and then to the US, and she came here under the name Sarah Kalmanowitz y Lev, confirming that her original surname was Lev, and also confirming that the name Lev was refashioned into Lavine here in the US, and that her married name was Kalmonowitz. At some point she divorced, and so in this country only used Lavine. This one person solved a months-long dilemma for me - what was the original Lavine surname?
As for entries/spellings of surnames - for the Lavine/Lev family above, Sarah Lavine has that as her main name. I have in her birth field that the surname was originally Lev. For her father Efroim, who did not come to this country, he is only listed as ' Efroim Lev'. Basically, I use the surname with the spelling that the person used themselves for most of their lives. I do not use Americanized forms of surnames or Americanized spellings for persons who did not come to the US.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus