I'm not really in the mood for a Samuel Smith's, so...
make it a Wig Top IA.
As explained at Wikipedia - India Pale Ale or IPA is a beer style within the broader category of pale ale. It was first brewed in England in the 19th century. The first known use of "India pale ale" is an advertisement in the Liverpool Mercury in 1835. It was also referred to as "pale ale as prepared for India", "India Ale", "pale India ale" or "pale export India ale".
While IA may not be a common initialism for the beer style, I can't help but think about beer whenever I pass the above pictured store due to the familiarity of IPA as an initialism combined with the unusual bullet point insertions in the store's name and the recent influx of oddly named beers.
Yellowpages.com lists the store's name as Wigtopia Beauty Supply. Even without the addition of "beauty supply", when the bullet points are removed it is much more clear that the store name is meant to be verbalized as one word with syllable breaks like so: /wɪg.to.pi:ʌ/. This was also confirmed when I phoned the store and the clerk answered as such.
Perhaps the store owners designed the signage to be phonetically playful. Wigs do top the head and they probably do sell what they consider to be the ideal wigs, thus: /wɪg.tɑp.i:ʌ/.
Regardless, I can't do it; I will continue to read the store name as two words and an initialism: /wɪg tɑp aɪ eɪ/.
India Ale image here
Wig Top image from Yelp