The only question is whether Watsi and BCBS operate within similar enough markets for their use to be considered infringement - I'm less sure of that.
On a related note, this is why early-stage startups shouldn't get too attached to their branding, product name, and/or company name. You're better off focusing your efforts on your product itself.
And don't waste money (as an early startup) on filing for trademark protection - because US trademark law respects common law use (ie, if you used it first, you are protected, even if you didn't file for protection)[1]. Registering your trademark does nothing if someone else (with more expensive lawyers) was using it first and can demonstrate that use.
And even if they accept your registration, that doesn't mean that it will hold up. Just like patents, the USPTO leaves this up to courts to decide. You could easily register something like the Coca-Cola[2] logo and they could accept it, but that doesn't prevent Coca-Cola from litigating against you and winning. They have no great way to check for conflicts, and they err on the side of issuing the trademark (and collecting your fee) so that the courts can be the final arbiters[3].
(Obligatory disclaimer: I am not a lawyer, and this is not legal advice).
[0] https://encrypted.google.com/search?tbm=isch&q=blue%20cross%...
[1] This is the opposite of the way that patent law works.
[2] In reality, probably not Coca-Cola per se, because it's popular enough that anybody reading your application would notice it, but a trademark that's very similar to an existing logo.
[3] If you're wondering, no, they won't refund your fee if your trademark is deemed invalid.