When a Netflix NFLX -4.19% subscriber selects a TV show to watch on the streaming service, the action usually starts right away.

But that’s not the case with ABC’s popular Thursday night drama “How to Get Away with Murder.” Subscribers streaming that show on Netflix first watch a four-second glamour shot of star Viola Davis alongside an even bigger ABC logo as a snippet of the network’s Thursday night theme music plays.

ABC's popular show ‘How to Get Away with Murder’ was able to secure rare promotional material on Netflix. Subscribers streaming the show first watch a four-second glamour shot of star Viola Davis inside the ABC logo as a snippet of the network’s Thursday night theme music plays. Photo: ABC

The pre-roll promotion is a rarity on Netflix. When Walt Disney Co. DIS -3.09% ’s Disney/ABC TV Group agreed to license the show, the media behemoth negotiated for the ABC promotion as well as similar vignettes on other Disney-owned shows on Netflix.

A logo and a few seconds of promotional video may not seem like a big deal. But as networks struggle to keep their brands relevant, making sure viewers know the origins of a show and where to go for fresh episodes is paramount. Also, if the network is identified, the hope is that users will eventually be able to search Netflix by network for content instead of just by show titles and actors.

“Netflix is a valued distributor that now provides robust cross-promotional opportunities for our networks and our series. It’s a win-win for both sides,” said a Disney/ABC TV Group spokesman.

A Netflix spokeswoman declined to comment.

In the past, Netflix has typically tried to resist requests for any sort of promotional branding effort at the start of the show. It also took a hard-line toward allowing a network logo on the title card of shows on its home page.

That has been a sore subject for some media executives whose shows are sold to the service including John Landgraf, chief executive of 21st Century Fox’s FX Networks unit.

“One of the things that bothers me about Netflix is they make darn sure when they make an original series like `Orange is the Black’ or `House of Cards’ that is identified with the phrase `A Netflix Original Series.’ They are equally staunch about totally stripping AMC off of `Mad Men’ or FX off of `Sons of Anarchy,’” Mr. Landgraf said at an industry luncheon last year. Until mid-2013, 21st Century Fox and Wall Street Journal owner News Corp were part of the same company.

A screenshot from Netflix's site menu lists ‘How to Get Away with Murder’ with its ABC network logo, while shows, such as ‘New Girl,’ carry no promotional logo. Netflix original series, such as ‘Orange Is the New Black,’ have the Netflix logo in the upper left corner of their title cards. Photo: Netflix

The title card issue is starting to fade. Many of the shows Netflix carries, including several from FX, now include the original network’s logo on the title card that users see when perusing the site’s menu.

However, not all TV shows on Netflix get special treatment like “How to Get Away with Murder.” As yet, there are no network logos or promotional pre-roll videos for CBS’s “Madame Secretary,” Fox’s “New Girl,” Bravo’s “Girlfriend’s Guide to Divorce” or the CW’s “Jane the Virgin,” to name a few. Pretty much all evidence of the shows’ original TV homes is nonexistent on Netflix.

“They are going to have to find ways to accommodate the needs of the people they buy shows from. The platform should be obligated to offer that little bit of branding material. I’m glad to see it going into that direction,” said the head of one major TV studio.

Keeping good relations with their major content suppliers may be taking on a greater priority at Netflix as of late. Some traditional media companies, including 21st Century Fox and Time Warner Inc., have indicated they are reconsidering their relationships with streaming platforms like Netflix.

In addition, Netflix is also contending with more competition as rivals Hulu and Amazon spend heavily to acquire content.

The heightened sensitivity over logos and promotions flies in the face of the customs in the traditional rerun business. When a cable network or local TV station acquires a rerun, it usually does not keep the logo of the network that originally aired it. For example, reruns of the CBS series “NCIS” on USA Network don’t carry the CBS network’s eye logo.

While reruns of new shows often take as long as four years before appearing on a local station or cable channel, streaming services get them much faster. “How to Get Away with Murder” and “Madame Secretary” are both only in their second season. The networks hope viewers who discover or play catch-up with their shows on Netflix will then start to watch episodes live or record them.

Netflix won’t automatically say yes to any promotion or brand request. One network has been pushing the service to allow time-and-day promotions that could run 10 seconds at the start of its shows. Netflix said no dice, according to an executive at the network.

Write to Joe Flint at joe.flint@wsj.com