It should, but not always so, maybe still in charter ?

Why are the funnel colours still in Rose line if there is a mane change and different owners surely the funnel would have be changed too

It is FALMOUTH CASTLE , I can read the name on the photo !

Thomas Rose/ Rose Shipping went into liquidation in 1917 but their ship Braeside was sold to Harris Bros. of Falmouth in 1915 and renamed Falmouth Castle. In 1923 transferred to Falmouth Castle Shipping of Bristol.
1927 sold to 'Soc. Anon. Les Caboteurs Algériens', of Algiers & renamed Cartenée. 1928 sold to Société Algérienne de Navigation pour l'Afrique du Nord', also of Algiers, & renamed Ville de Ténès.

So if its Braeside (built 1909) the photo date/ name is wrong ... it does say circa 1919 so could it be "Rose" ship grounding pre 1915.
Finally wrecked 1951 after serving as WWII auxiliary minesweeper and possible conversion to wine tanker.
Info from "THE SUNDERLAND SITE" /PETER SEARLE'S WEBSITES

Also see http://sunderlandships.com/files/201502241309190.BRAESIDE1909.jpg
More convincing this is Braeside .. funnel markings and size of name/spacing on bow.

Location is undoubtedly Porthcurno Beach. The several copies of this photo or similar ones all give the name as FALMOUTH CASTLE. On 'original size' the space in "...H C..." can just be made out nad the name is too long for BRAESIDE.

No reports of BRAESIDE ever going ashore in Cornwall have been found. FALMOUTH CASTE was put on the beach on 17 March 1919, when sinking after striking a rock, and the crew were saved. She was eventually refloated on 1 April after bottom damage was patched and towed to Penzance.

This ship is Braeside 1909 owned by Thomas Rose of Sunderland and has Rose funnel marking
The name on bow is only one word

See https://wrecksite.eu/wreck.aspx?244725 for more details

Thanks Krispen

"FALMOUTH CASTLE". This is Porthcurno Beach, on the west side of Mounts Bay. She grounded there in 1919. This is from the Gibson collection.