As far as longest tenured NA regiments, go . . .
1stRddt and 87th are MM regiments (well, the reddits were a brigade that just sort of just acts like a regiment now to deal with lower numbers) that are still in NW. The 87th left briefly for Holdfast and then came back, but they never disbanded. Neither of them have changed their name once to my knowledge, nor have they taken extended hiatuses from linebattle games.
There are several regiments that formed in MM or NW that never disbanded, but moved to other games and are still functioning, like the 1stEPI and the 33rd. I wouldn't count this, except that I want to take every opportunity to remind people that the 1stEPI existed, and that the NA community largely exists because of them and 5arge.
I still think of the LIR as a new gen regiment, but they formed in late 2014, so they're six years old now. Again, no name changes or hiatuses. The Nr9 formed a few months earlier, although they spend more time in Holdfast than NW now and had a month or two of strictly Holdfast.
There's the RKR, they've been around since 2012 and play in four regions. They did take a several-month vacation some years back and had a rename, for what that's worth.
Special mention to the 00th. They're not operating currently in this dimension, but I don't have hard data on what Thundersnow's space-time manipulation did to their length of time as a regiment.