Brand names cannot be changed when cited or referred to in writing. However the brand name is written or spelled, it must stay that way even if it means starting a sentence with a lower-case letter.
So, easyJet is the brand name and EasyJet, both used by the company and eBay. So, either one, I'd say.
easyJet is an interesting company.
eBay is a corporate behemoth.
But editors will often reword a sentence to avoid this, as explained below.
Quote from ragan's PR Daily:
"eBay has a fabulous collection of vintage tube tops. iTunes must now compete with Amazon’s Prime Music.
The Chicago Manual of Style has this to say: “Brand names or names of
companies that are spelled with a lowercase initial letter followed by
a capital letter (eBay, iPod, iPhone, etc.) need not be capitalized at
the beginning of a sentence or heading, though some editors may prefer
to reword.” That wasn’t always its rule, though:
This departure from Chicago’s former usage recognizes not only the
preferred usage of the owners of most such names but also the fact
that such spellings are already capitalized (if only on the second
letter). Company or product names with additional, internal capitals
(sometimes called “midcaps”) should likewise be left unchanged
(GlaxoSmithKline, HarperCollins, LexisNexis):".
Summary: Brand names are legal names and cannot be changed in writing.
The Bestselling Guide to English Usage
company names Call companies by the names they call themselves. Here
is a selection of names that are sometimes spelt incorrectly.
AT&T (American Telephone) [see the full list in the PDF]
Refer to the full guide here:
The Economist Style Guide