Blockchain developer would probably suit you if you want to make a career out of bitcoin or you can probably do this thing where you ask the management or the payroll of your company that you're working on to pay you in bitcoins, that technically counts as you building a career with bitcoin since you're getting paid with bitcoin. So to answer your question, yes it's possible to build a career in bitcoin.
It's not relate to Bitcoin, become a Blockchain developer mostly involved in Altcoins ecosystem, not Bitcoin.
Getting paid in Bitcoin and work in Bitcoin are two different thing, you can get paid in fiat and use that to buy Bitcoin, the result is same.
Most of developers in Bitcoin are volunteers where they're not expect any payment, unless they're miners, consultants or speakers in seminar.