I almost always advise not spending out-of-pocket funds on "branding." Here's an analogy that explains why.
Britain was faced with an artificial dilemma during WWII. It had limited air support and associated firepower and needed to decide how to use it. A "tactical" approach would protect Allied offensives and defend military assets; a "strategic" use would attempt attempt break the will of the German people by bombing their cities civilians--as the Germans had been doing most famously to London for some time.
I remember learning about this in high school and thinking it was a bit of no-brainer. On one hand a tactical use would protect a supply convoy or offer air support to a ground offensive. And on the other hand a supposedly "strategic" use would bomb mostly German civilians housed in centuries-old towns--a misguided Hail Mary pass to break the will of one's enemy as if that has a real measurable result. I didn't understand why the latter option was even seriously considered--let alone executed to what is generally--and admittedly, in hindsight--understood to be disastrous effects. It needlessly prolonged the war and significantly increased military and civilian casualties--as well as destroyed countless artistic and architectural wonders.
And what is the value of a "broken will" over increased likelihood of a campaign's success or decreased military casualties for the Allies? And then of course there is the pesky moral issue of bombing mostly civilian areas. Let's ignore that for the purposes of this nonprofit arts blog.
In my adulthood I became more familiar with making decisions in a "siege mentality" or in an environment of scarcity which can be, far too often, the places in which nonprofit arts administrators find themselves. With limited resources--time and money mostly--one begins to reach for silver bullets, all-in-one solutions and easy (though obviously very expensive) answers.
So the "strategic bombing" choice makes more sense--though remains just as troubling. I'm aware of multi-million dollar budget arts organization which, on the brink of closing the year prior, had set aside a six-figure budget for "organizational branding" the following year. Prior stakeholders had approved that investment in hopes it would "turn the tide" of slow sales and serve as a kind of silver bullet solution for the theater. This is an example bad strategy impeding good tactics. It is also an example of an easy and ill-fitting solution being offered to a complex problem requiring a much more simple--but harder to execute--fix: just advertise better. Dig into your marketing data, make adjustments, and optimize further.
The best branding an arts organization enjoys is a full house enjoying robustly-advertised programming. This fills the organization's database with new-to-file patrons for marketers and fundraisers to further engage in a loyalty or other plan.
While this statement is slightly hyperbolic, I generally mean it: a nonprofit arts organization should only invest in a specific "branding" effort when every seat to every event is filled. Branding is an exercise in luxury.
This is not to say your nonprofit arts organization should not have a brand; it is to argue that what you do (your programming) is pretty much who you are. Do you think Steppenwolf (arguably one of the strongest brands in nonprofit theater) in its early, "brand-building" days invested in a branding agency or consultant? No, they DID their brand. They PERFORMED it and with enough repetition, experience, and exposure (essentially advertising) of what they performed, they built a "brand." I don't even like to use that word. Ugh.
I am reminded of an Carey Perloff anecdote of her, in the midst of A.C.T. literally falling apart due to a recent earthquake, being asked by a strategic planning consultant, "If you were a kind of vegetable, which would you be?" Branding is of little value if you are operating at 60% paid capacity.
Nonprofit arts organizations do need logos and they need style guides (both for language and design). This is not an argument against strategic planning and promoting heuristics to help your patrons and potential patrons absorb more quickly who you are and what you do. But in an ideal arts organization, these two "who and what" characteristics are already aligned.
And indeed, the Steppenwolf of today--now many decades older, in a new space, operating at a much higher budget, etc.--may find the need for some investment to help sharpen their branding focus.
My point is that there is no better brand ambassador than a new buyer who saw your most recent event and recommends it. Focus on the patron--not intermediate metrics like "unaided recall" and other luxuries--and your strategy organically develop.