I was looking for some other information completely when I came across the top 12 LCMS church names:
Trinity - 569
St. John - 467
St. Paul - 464
Immanuel - 325
Zion - 323
Grace - 235
Faith - 221
Our Savior - 168
Redeemer - 168
Christ - 144
Good Shepherd - 136
St. Peter - 131

Add to that the other Lutheran churches with the same name, as well as other Christian churches with the names, especially with a name like Trinity.

There's nothing wrong with being Trinity Lutheran Church. Your url is what might suffer. trinity.org, trinity.com, trinitylutheran, trinitylcms, etc. They've been taken for some time, so if you're looking to start a new congregation, it might get tricky to find a solid, short url for your website.

And what about .com or .org? The church I attend is gracelcms.com, while gracelcms.org is in Minnesota. Then grace.org looks like it's non-Lutheran, and grace.com is a business website. You have gracelutheran.org in California with a 2011 website. Then there's gracelutheran.com in Red Lion, but I can't find the address very easily on it's Wordpress site with Dreamweaver-ish menus (I can see the donation link right away, so I guess that explains the .com). You can find gracelutheranchurch.org in Minnesota, while gracelutheranchurch.com is in PA. I built graceserves.org, so that's a way to get creative. In my own city, gracejax.org is for Grace Community Church (non-Lutheran), while gracejax.com is kind of a non-website that is seemingly owned by a church but not developed.