As a graduate student, is it better to use a Gmail address or name@mywebsite.com? As a grad student (Note: I am in the humanities, so nobody is really technically inclined), I have an address from my institution (.edu) but I rarely use it. I suppose I do "use" it, but it forwards to my gmail and usually I reply with my gmail address. Almost all of the other grad students, as well as many professors, in my program -- and elsewhere in my field -- do something similar; they don't use their edu addresses, but instead exclusively use gmail. I have been increasingly wary of Google's oversight and have been thinking about switching. But: Considering Gmail's monoculture among academics, is it more "professional" to use a Gmail account, or one that you personally own such as myname@myname.com? Or just weird?

To be clear: This is not about which email address to attach to a publication. That would clearly be my edu address, as it forwards to gmail. This is about what it 'says' about me.
I don't know how people view things in the humanities, but in mathematics having your own domain named after you sounds a little presumptuous, at least to me.  Some people do, and I find this normal for people like  writers or some programmers, but not most types of academics.  In addition, sometimes these go defunct because people stop renewing them, so something like gmail is a more "stable" solution.  If you dislike gmail and don't want to use your institutional address, check out some other email providers (yahoo, zoho, mail.com).

Note: to me, instituional addresses still seem more "professional" than something like gmail, but sufficiently many people use gmail for professional reasons that it doesn't look strange to use it.  In fact, something like gmail is often a better choice for young people who haven't settled down and may change their institutional address several times.