A genuine question for my non-Catholic friends, with absolutely zero flippancy intended: Can anyone (like myself for example) - start a church, just as so many have done for the last 500 years, and call his or her new church the church founded by Jesus Christ?
Disclaimer: I am not officially Catholic (waiting on a priest to contact me about catechesis), but have ceased protesting
To the OP: one thing Catholics must keep in mind is that, in the Protestant mindset, there’s generally no authority or “permission” if you will needed for the founding of a new denomination or a new independent “community church”.
This has not always been the case, and still may not be for some. For example, many people were scandalized by Wesley’s action of ordaining other men in his day (he was an Anglican priest, and lacked the authority to ordain in the C of E as he was not a bishop).
For a current example, I saw a debate between a Catholic layman and a Protestant minister who started his own independent, non-denominational church. In a Q&A session in the debate, someone asked who gave him the authority to found his own church. His reply was that he didn’t, Jesus founded the church and called him to pastor this congregation.
This sort of detachment seems to be common, at least among people who say Jesus wanted to build a church. They acknowledge that, but usually quickly follow with “but He sure didn’t just found one true church” or something to the effect that He really intended to split up his followers, contrary to what He said.
Then you have some churches that are adamantly (and ironically) anti-church. An example is Calvary Chapel. As a group, they tend to be so anti-ecclesial that they talk about how any structure is a necessary evil and should be as limited as possible. They also tend to deny the value of ritual, tradition; etc. Talk about throwing the baby out with the bath water…
(Note: I was part of a CC congregation for a number of years, including being ordained as a youth pastor, before coming to the point I’m at now. I am grateful for what God has taught me in CC. They’re big on submission to authority, even though they preach against ecclesial authority

)