Came across this pic on internet. Marked as "public house Birkenhead 1900"
Any idea what its name was?

This is a list of Yates Castle Pubs in Birkenhead, some of them are easy to cancel out.

Above the door is the name "Porter" and the window next door has "Dairy"

Manor Hotel, Union Street, Tranmere, Birkenhead
Charing Cross, Grange Road West, Birkenhead
Copperfield, Market Street, Birkenhead
Imperial, Derby Road, Tranmere, Birkenhead
Letters, Argyle Street, Birkenhead
Old Colonial, Bridge Street, Birkenhead
Royal, Woodchurch Road, Birkenhead
Windsor Castle, Oxton Road, Birkenhead
York Hotel, Birkenhead
Park View Hotel, Birkenhead
Market Tavern, Birkenhead
Forester’s Arms, Birkenhead
Haymarket Vaults, Oliver Street, Birkenhead (owned 1903)
Ivy Hotel, Birkenhead (owned in 1903)
Scottish Chief, Brook Street, Birkenhead (closed 1904)
Egremont Tap, Egremont, Birkenhead (owned 1892)
Odd- licence, 444 Borough Road, Birkenhead
Mersey Arms, Birkenhead (rented 1896 on yearly tenancy terms)
Duke of Edinburgh, Cleveland Street, Birkenhead (owned 1912)
Old Post Office Vaults, Argyle Street, Birkenhead
Angel Inn, Beckwith Street, Birkenhead
Clarendon Hotel, Chester Street, Birkenhead
Claughton Hotel, Upton Road, Claughton, Birkenhead
Cleveland Hotel, Cleveland Street, Birkenhead
Dock Hotel, Freeman Street, Birkenhead
Fireman’s Arms, Oliver Street, Birkenhead
Forester’s Arms, Patten Street, Birkenhead
Hamilton Vaults, Hamilton Street, Birkenhead
Hamlet Inn, Chester Street, Birkenhead
London Hotel, Canning Street, Birkenhead
Manor Arms Hotel, Chester Street, Birkenhead
Rose & Shamrock, Laird Road, Birkenhead
Wirral Hotel, Cleveland Street, Birkenhead

I can't find any info on Yates's Manchester Ales.

The players were,

William Yates & Co Limited
Castle Brewery, Ardwick, Manchester,

Gatehouse and Yates, amalgamation.

Below, the number of licenses held in 1891 and the brewery location.

Why put 'Yates's Manchester Ales' on the pub instead of Yates Castle Ales?
Or why not put Yates's Ales, Manchester?

Possibly promoting the ale was peculiar to Manchester, perhaps a distinctive taste unlike others.

There were at least two different brewery companies with the name Yates in the Northwest, it was common to refer to Yates Castle as Yates Manchester.

The company was William Yates & Co Limited, the brewery was the Castle Brewery, Manchester, various branding was used.

Off the 1899 pub drinking map

Neither of them was as good as Birkenhead Brewery Ale, mind you I was weaned on it.