It is whatever you want to call it. I'll give a few ideas.
A term you might be looking for is a "spread", especially a "synthetic spread". This generalizes any combination of products that itself isn't directly traded on the market, but may or may not be related to a product that is traded.
If you have an arbitrage position whose profit can be locked in by trading out another leg, you'd most often call it "unhedged", "inventory", "residual" etc.
Depending on how you've structured your software and how your traders communicate, it may make sense to name "synthetic order types", which themselves aren't provided by the market but can be emulated by combining more than one explicit order type - for example, a "buy spread", "buy butterfly" order type etc. In that case, you could say that you're "working a spread" or a "spread order" is "partially filled" if not all legs of a spread are executed.
But most commonly, you'd just refer to any executed orders as part of your "position(s)", and any unexecuted orders as "orders". Ask your FX dealer or prime broker to show you their GUI platform and you'll probably understand what I mean. There's no conventions for referring to any triangles etc. Under "position(s)", you could either look at things net-by-currency or net-by-currency pair. The reason for this is that spot transactions need to be closed out or rolled on value date, and say if you are long EUR/USD, long GBP/EUR, long USD/GBP, you could:
say you're just long USD (net by currency) and closing that out only involves converting to your account currency, or
say you're long 3 pairs and close out by selling all 3 pairs.
At my firm we usually have a few standard names for common linear combinations of products, like 1-2+1, etc. a symbol convention for these, and our FX counterparties probably wouldn't understand what we mean if we used the same lingo with them.
A possible arbitrage strategy is to combine the currency prices in pairs
It's hard to understand what you mean by "combine the currency prices in pairs". Could you clarify?
Spot FX prices are quoted in pairs of a base currency and a quote currency, e.g. EUR/USD. Conventionally, you won't find an inverted pair, i.e. USD/EUR in this case, being traded as a separate product on an ECN or other liquidity pool, so that arb doesn't exist. Combining any 2 pairs like EUR/USD and EUR/GBP isn't an arbitrage since all you're doing is picking up currency risk. Do you mean a triangle?