Double trouble today! The name 井芹 is usually Iseri or rarely Izeri, and 増井 is Masui or rarely Mashii.
I did wonder if it was one of those fancy two-way nameplates, but unfortunately, while 芹井 is a surname (read Serii), 井増 does not seem to exist. (You might even say...... いません.) Sorry :)
井, which both names share, is very common in surnames. It means well (as in a well water) or town/community. It's read い, セイ, or ショウ.
芹 is new to this blog! As the grass radical 艹 suggests, it's a herb, called seri or Japanese parsley. It's read せり or キン, the latter of which it shares with its other radical 斤, meaning axe.
増 means to increase, add, augment, gain, or promote. It's read ま.す, ま.し, ふ.える, ふ.やす, or ゾウ, the last of which it shares with its right radical, 曽, which means formerly, ex-, once, before, or ever/never.
Stopped in my tracks and gasped at this pair of nameplates! The similarity wouldn't even have occurred to me if they hadn't both added rōmaji! 増井 is usually read Masui, rarely Mashii, while 松居 is usually read Matsui, rarely Matsu.
増 means increase, add, augment, gain, or promote. It's read ma.su, ma.shi, fu.eru, fu.yasu, or zō.
井 means well. It's read i, sei, or sho.
松 means pine tree, and it's read matsu or shō.
居 means to reside, exist, be or live with. It's read i.ru, i, o.ru, kyo, or ko. It's the verb 居る (iru) to be/to exist/there is (used for living things),
I love coincidences like this and have seen a few in the past, so Im putting together a new tag: #goodneighbors :)