at first, it might seem that way, but maybe that's not the real problem.. it happens in .com too.
if wordglobal.com is taken, you might try something like word-global.com.
if global isn't very important to your name, but you want the same idea, you can go with wordinternational.com.
.international does seem like a silly extension though.
you could buy SacramentoPhoto.com, and someone else could be using SacramentoPhotography.com, SacramentoPhotographer.com, Sacramento-Photo.com..
but the great thing about .com and others is they give you quite a bit of flexibility when your name is taken.
maybe there are 20 companies named PhoenixDesign.
if Phoenix.design is taken, what are you supposed to do? you probably don't want a weird-looking name like WeArePhoenix.design or.. PhoenixInterior.design, if that's your niche. I guess you only have a couple other decent options like phoenixdesign.group.
in .com, you can do all kinds of things, and the domain will still be memorable enough.
designsbyphoenix.com
wearephoenix.com
phoenixdesign[location].com
phoenix-design.com
[some memorable phrase].com affordabledesign.com
flywithphoenix.com
phoenix[something]design.com phoenixinteriordesign.com
tryphoenixdesign.com
or you can use any other generic extension without adding a random word to your name..
phoenixdesign.org, .co, .io, .net, local .ccTLD,...
instead of .services, .solutions, .group, .whatever.
even the most generic new TLDs are a bit silly.
.website
.site.. .online.. yes, we know we're online
.xyz