To put it mildly, the Washington Redskins have a branding problem. There are new calls from numerous organizations to change their name because the term “redskin” is considered a racial slur by many Native Americans and others. The team’s owner has vowed to “never” change the name. Some sportswriters have vowed never to use it again. This case of brand name questionability is particularly interesting because changing it or not changing it would likely have little effect on team revenue, fan loyalty, or the performance of the team. The conflict is largely political, ethical and philosophical.

But the dilemma that the professional football franchise in Washington now faces is not unlike what many brands will face at some point in their evolution: When is the right time to change your brand name?

It may sound easy to say, “change it” when it’s hurting you more than it’s helping you. But it’s not that simple. There are two reasons for this. First, changing a brand name because a growing audience dislikes it still carries with it the opportunity cost of losing the remaining audience that thinks it’s just fine the way it is. And this audience often represents a brand’s most loyal and profitable customers. So, the positive effect of changing a brand name to please a vocal minority may have the far greater negative effect of disappointing or alienating a core customer base.

Secondly, it is generally next to impossible to quantify the pluses and minuses of a name change. For instance, a company may begin to hear anecdotal evidence that people are deciding not to call them because of a negative association they have with the name. That’s always unsettling. But trying to accurately estimate how many people didn’t call because of the name is hugely difficult, if only because many people may not even consciously be aware of it to begin with.

So many times a brand will find itself in a kind of brand purgatory where they know their brand name is a negative or a drag on their performance, but they don’t feel comfortable risking the equity in their loyal customer base that would come from changing their name. Because of this, brands that change their name must essentially take a leap of faith in deciding when to shift to a new name and when to stay put.

Some choices are easier than others. When Federal Express made the change to FedEx in 1994, there was hardly a ripple. Their customers had adopted the shortened name years before, and the company continued to include the original name in smaller type under its new logo until the year 2000.

In contrast, Kentucky Fried Chicken found itself at the wrong end of a cultural shift that placed greater scrutiny on the negative health consequences of fried foods. The “finger-lickin’ good” franchise ran for cover by adopting its initials as a day-to-day brand with the hope that removing “fried” from their name would bring them more sales. This was, at best, a cosmetic move until they developed healthier choices, such as their grilled chicken menu items.

A brand can be fantastically unlucky, as was the Ayds Reducing Plan when a phonetically identical acronym was established for the emerging disease Acquired Immune Deficiency Syndrome.

But a recent brand name change may serve as a potential guide to brands that are debating the value of a change.

YouSendIt, which began its life as a file sharing service, recently changed its name to Hightail. The move was described by their CEO as a look to the future, which already has many features beyond the file transfer world and now includes cloud storage and other business services. While YouSendIt was well known, the name threatened to limit the perception of their product line in the future. And therein lies the principle that many brands can use for inspiration.

A brand’s managers can ask themselves one or two questions. Try this one: Five years from now, do we think we will have grown and remained sufficiently profitable with our current name? Or ask this: If we were starting a new company right now, how would we brand it? If either of those questions point toward making a change, it’s likely time to get started on a new brand name.

The Washington, D.C. pro football team might do well to ask themselves the two questions above, especially the second. Changing a brand name is never easy, but sometimes it becomes inevitable.