Announced in March, the takeover will trigger a little-known right inserted in the listing particulars of BG and Centrica when the two companies were demerged in 1997.
The change-of-control clause would have allowed BG to acquire the UK rights to the British Gas name if Centrica had been the subject of a takeover, insiders added.
The deal would allow Centrica to use the British Gas name outside the UK, which executives are understood to be keen to have the right to do.
"The brand is extremely well-known, and not just in the UK," said one source.
"There is optionality for the company to consolidate the rights to it."
For Shell, the proceeds will not go very far towards the $30bn (£19.5bn) earmarked from disposals after its takeover of BG Group completes next year, with sizeable assets around the world expected to be offloaded at a time when the oil price is expected to persist at the current subdued levels.
Mr Conn is busily attempting to reshape Centrica after taking over from Sam Laidlaw at the beginning of the year.
At this week's annual meeting, a large minority of shareholders expressed discontent at the multimillion pound sum handed to Mr Conn to compensate him for earnings forfeited at BP, his previous employer.
People close to him pointed out that he had accepted a substantially lower overall pay deal than that enjoyed by Mr Laidlaw.
In an interim management statement published on Monday, Centrica said it was trading in line with earlier guidance, "with improved year-on-year profitability downstream expected to be more than offset by the impact of lower commodity prices on the upstream business".
The company also warned that its earnings "remain subject to the usual variables of commodity prices, weather and asset performance, and the uncertain outcomes of the UK General Election and the Competition and Markets Authority investigation into the UK energy market".
The competition inquiry is due to report on provisional remedies shortly after next week's General Election.
Centrica declined to comment on the prospective deal to acquire the British Gas name.